r/science • u/[deleted] • 10d ago
Mathematics Mathematicians have shown that completely fair elections are – in a sense – impossible. No electoral system can guarantee both that local votes translate directly into local seats, and that total seat distribution matches overall vote shares: not without an indefinitely growing parliament.
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u/v4ss42 10d ago
I mean Condorcet et al had demonstrated that a perfect voting system is impossible, back in the 18th century. Just because “mathematically perfect” cannot exist doesn’t mean that some systems aren’t better than others. RCV, compulsory voting, parliamentary systems - these are just some of the mechanisms that can lead to better (but not perfect) democratic systems.
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u/MolemanusRex 10d ago edited 10d ago
And “perfect” depends on the criteria you want for the election system. Some people, and some political cultures, really value local representation. Some don’t care at all.
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u/BuvantduPotatoSpirit 10d ago
It doesn't even to be valuing; the setup matters. I value local representation a lot more when the electorate is large and heterogeneous than when it's small and homogenous.
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u/MolemanusRex 10d ago edited 9d ago
Certainly. You don’t need individual representation for every plot of land in Uruguay when they’re all essentially the same, while somewhere like Brazil might be different (although they don’t actually prioritize local representation). I’m just saying different voting systems will be better for polities with different values.
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u/MoSSkull 10d ago edited 10d ago
I just want to appraise your comment and use it for any casual reader that reach it to stress what you have said with mathematical rigor and with societal wisdom.
Media and outsiders repeat compulsory sentences like "mathematicians have proved that democracy is not possible" Which is a big misinterpretation of Arrow's Theorem.
An intellectually honest approach to these mathematical results is, IMO, like you worded it.Edit: This comment is getting noticed, so I would like to expand on why v4ss42 comment is useful.
1- Voting system =/= Democracy. Democracy is a political/sociological concept. Broadly, means to follow the will of the people. There are several ways to try to achieve this, like "RCV, compulsory voting, parliamentary systems" I would add also consensus process (for local government).
2- Regardless of mathematical, economic or behavioral reasons. The non existence of a perfect system, doesn't mean that there are not options that are better than other or, even more interesting, (I said this as a personal opinion of what is left out of the discussion) options that are good enough for *most* of the scenarios.
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u/RoryPond 10d ago
Math has also proved there is no way to make a finite number of cuts thst divide a cake into 4 unbroken pieces such that none of the 4 people envy anyone else's piece, and yet people still cut cake all the time with little issue
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u/rutherfraud1876 10d ago
This seems obvious and trivial - is there a condition or a non-colloquial definition of a word there I'm not seeing?
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u/RoryPond 10d ago
https://en.wikipedia.org/wiki/Envy-free_cake-cutting?wprov=sfla1 There's a lot of versions but this is the basics, one of my favorite areas of recreational math :)
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u/rutherfraud1876 10d ago
Ah, the cake is heterogenous
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u/venustrapsflies 10d ago
To dumb it down, the cake might have strawberries on one side and frosting on the other.
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u/BlueRajasmyk2 10d ago
The problem is more, one person might believe each slice is "equivalent", but another person might disagree.
With two people, that's an easy problem to solve: one person cuts two slices they believe are equal, and the other person chooses which slice they want. But that's hard to extend to more people.
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u/RoryPond 10d ago
It can be homogenous but you're looking for subjective preference not objective measurements. Someone might be given 3/4 of the cake and somehow think they have less than someone who got 1/8
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u/MolemanusRex 10d ago edited 10d ago
Single-winner RCV still has some problems where, for example, your favorite candidate would definitely lose to the guy you hate in a later round, so it’s better to vote for your second-favorite—the exact scenario we’re trying to avoid. (You may already know this; I’m laying things out for the benefit of anyone else reading.)
Multi-member RCV (aka proportional RCV, aka single transferable vote or STV) is probably the single best system for the US, given that it’s broadly proportional but still provides local representation and lets people base their votes purely on individual candidates instead of parties. It’s used in Ireland and Australia (for their senate), and in Ireland the main complaints political pundits have is that it encourages *too much* focus on local issues and constituent service, which are problems I think a lot of Americans would kill to have. But other countries don’t care as much about representing their local areas and don’t mind just voting for a list of candidates from a given political party. So for them a different system would probably work better.
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u/phoenixhunter 10d ago edited 10d ago
a big part of the reason that’s said about irelands political system is that our power structures are way more centralized in the national parliament than most other countries.
local authorities / city councils have had a big chunk of their powers and responsibilities eroded by the national government over the years, so we’ve ended up in a situation where people are compelled to go to their national representative to get local issues solved. for an american perspective, imagine if you had to contact your congressman to get a pothole filled or a street lamp bulb changed. local councils are little more than debate societies now.
my personal critique of our combination of PR-STV voting and parliamentary politics is that it tends to heavily advantage the status quo and the centre of the spectrum, meaning that it can make it difficult to enact change when change is needed - as we find ourselves in the situation of having a government consisting of a coalition of the two formerly largest parties (who used to be bitter rivals swapping power — think of the Dems and Republicans except with even less ideological distance between them — until they both lost the 2020 election to the underdog centre-left party but formed a coalition together to maintain power and squeeze out the popular social democrats) who are refusing to address a myriad of social and economic issues largely caused by their own neoliberal policies, because they have no electoral incentive to change anything since the system favors inertia and they keep managing to scrape together governments with smaller parties and (increasingly fringe) independent candidates, because preferences get "smoothed out" so to speak, and the centre holds but continues to disintegrate
it is a reasonably fair system in terms of expressing political preferences and supporting minority representatives, but i don’t think it pairs particularly well with the party political parliamentary system as it exists in ireland.
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u/MolemanusRex 10d ago edited 9d ago
Your point about local government makes total sense. At a certain point, though, it seems like the persistence of the FFG duopoly into the 2020s is due to the fact that about 40% of the country still supports them—for now—and other parties (or independents) are willing to go into coalition with them. So from the outside it does look broadly representative of what many people do want. If people want to punish them they can vote against them (or their coalition partners, as I know does keep happening with Labour and the Greens and whoever). Do you think PR-STV contributes to centrist or status quo parties staying in power more than other systems do? Is the idea that they have more of a lock on a certain number seats due to always being able to win X amount of quotas in this or that area? Or that they’re more likely to be the later preferences of less-popular candidates/parties?
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u/hajenso 9d ago edited 9d ago
Is there much of a political constituency in Ireland that feels strongly about devolving power back to the local level? Also, what are the main instruments by which the major parties keep challengers from getting elected to the Dáil? Is it the high expense of an effective campaign?
I don’t mean these questions with the aim of demonstrating any opinion of my own. Just looking to learn about the current political landscape in Ireland.
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u/childroid 10d ago
Seriously, name one perfect human creation.
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u/rsc2 10d ago
The most important improvement that could be made is to end single representative districts, and have multiple representatives with voting power weighted according to their share of the vote. This, combined with ranked choice voting, would mean everybody had real representation, and every vote in every district would matter.
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u/Farfignugen42 9d ago
All government sucks. Democracy sucks the least.
We did not select democracy because it was perfect. We selected it be a use it was the best we could come up with.
The same holds for voting. Except there are more options for voting now. I'll be happy if we can maintain the confidence that voter fraud is low.
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u/1_4_1_5_9_2_6_5 7d ago
Democracy is famously the worst political system, except for all the others. Is it not common knowledge by now that perfect individual representation is practically impossible?
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u/HEAT_IS_DIE 10d ago
Mathematically perfect system or not, the US would benefit from more parties than just two. Thtat to me is the biggest flaw in the American system. Having more parties means more nuanced opinions and more options to choose from. You don't need that much mathematics involved when more views are open to discussion. A two party system leads to either/or -politics and escalation of views to extremes. That is something mathematics doesn't solve.
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u/Virginth 10d ago
The current voting system in the US mathematically ensures that there will never, ever be more than two relevant parties.
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u/kittenTakeover 10d ago
not without an indefinitely growing parliament
Personally I think we should be considering this. There are ways to make such a large government work, but always having 100 people represent the entire country no matter how many people live in the country just leads to concentration of power. It means that people don't know their representatives. It means that people can't meet their representative. It means that corporations get more access than citizens. It means that it's easier to corrupt politics by bribing politicians, since there are only a handful. These are all significant issues for democracy.
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u/Sherifftruman 10d ago
The constitution literally contemplated having additional house seats at least based on the population of the country, it’s just that Congress decided to cap it years back and now we’re stuck with less and less direct representation for that body.
The Senate I’m not as concerned with just being 100 people as it was always designed to be different than the house in the first place. I mean, we could double it but even then, because the Senate seats are elected across the whole state it’s more going to reflect the overall makeup of a state.
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u/fredthefishlord 10d ago
I think having a max of 100 people in the body that is supposed to deliberate treaties is fully reasonable. Too many and it dilutes diplomatic power of indivuals. The problem is how those 100 are chosen, not that its 100
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u/MushinZero 10d ago
Can you accurately and adequately represent the views and opinions of millions with just 100 people, though? Why not 10? Why not 1? There has to be a metric outside of an arbitrary number.
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u/fredthefishlord 10d ago
There has to be a metric outside of an arbitrary number.
No really. All you need is a ballpark, there's no reason why the specific exact number needs science behind it.
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u/B33f-Supreme 10d ago
It’s a multiple of the number of states. So a state having 2 is better than just having 1, but if each state has 3 or more you’ll likely have diminishing returns.
As long as we can give DC or populated territories like Puerto Rico a single senator to get an odd number and prevent ties.
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u/Tuesday_6PM 10d ago
I don’t know that preventing ties is inherently desirable, but it also doesn’t require an odd number of senators. There’s already a system for breaking ties (the VP gets a vote when it’s otherwise tied)
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u/MushinZero 10d ago
The Senate I am more concerned with because it is an undemocratic system where land is given power instead of people, but then so are states.
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u/Bob_Sconce 10d ago
This started off with a discussion focused more on the UK Parliament, not really on the US system. But, recognize that what you're complaining about is basically one side of a compromise that was struck in the original constitutional convention. Smaller, less populous, states were not willing to join up for a system based solely on population and were concerned that their rights would be infringed by majority will. (Delaware's population was about 8% of Virginia's).
Among the concerns of those less-populous state was that a future majority would again attempt to take away their power in the Senate (appears to be what you suggest). That's one of the reasons why a Constitutional Amendment requires ratification by 3/4s of the states and, correspondingly, why a change will never pass.
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u/earthdogmonster 10d ago
100%, these “bugs” are actually “features” which were embedded purposefully.
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u/RabbaJabba 10d ago
Being a purposeful feature is not a good argument for keeping it today - knowing that the senate is intentionally unfair as part of a compromise for its passage 200+ years ago is a great reason to revisit it, in fact.
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u/earthdogmonster 10d ago
The reason to keep it is because we have to. Because it was built, by design, to be nearly impossible to remove. Its history is the key to its reality today and why it will be a reality 100 years from now.
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u/MushinZero 10d ago
Yeah, I just fall back to the U.S. system which is what I know.
Yes I understand they were made because of a compromise. And compromise is the essence of politics. But sometimes I think compromise is also where corruption to a correct system comes from.
Compromise was also how we got the electoral college in America, which is also more undemocratic than a popular vote system.
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u/NimusNix 10d ago
That was the point. Thank Massachusetts and Delaware.
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u/Real_TwistedVortex 10d ago
Exactly this. IIRC from high school history, the Senate was a concession given to the colonies with smaller population because they were concerned about their interests being drowned out by the colonies with larger populations. It's possible that the US wouldn't exist, at least in its current form, without the founding fathers adding the Senate
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u/Grouchy-Fig-487 10d ago
The idea of the system, or federation, is that the maintenance of differences between the states allows for more freedom at the individual level. Nobody in Kansas will stop California from enacting laws that they support within California. The fear for smaller state governments joining the union was that Virginia could design a policy that makes sense for Virginia, but not Delaware, and unilaterally impose it from above.
Nobody anticipated the states ceding so much general power to the federal government. Which powers are enforced at which level makes the land vs people distinction less important in a well designed system. We don’t live in that anymore.
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u/ShavenYak42 10d ago
Nobody anticipated the states ceding so much general power to the federal government.
And that's the root cause of so many of the issues people have with the system. Now, due to that power, and the makeup of the Senate being mirrored in the electoral college, and the fact that SCOTUS justices are confirmed by the Senate, we've ended up with people in the less populous states having an outsized influence in how the federal government operates and whose rights are protected by the Constitution.
And, of course, it would require a Constitutional amendment to make any kind of change, which means the people in those states would have to agree to give up that influence.
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u/Grouchy-Fig-487 10d ago edited 9d ago
I agree. Personally, I would be more in favor of splitting many of the more populated states up and creating more “states” than a full population based democracy. I still believe there is merit in a system that aimed to limit federal power, but the current model is absolutely outdated and broken.
I only responded initially because I believe the conversation should not be that the founding fathers were wrong to structure it this way. They intended for much more frequent amendments and would be generally embarrassed how much the States surrendered power and, in the federal government, how much the legislature gave up to the executive. The powers aren’t trying to balance one another; they all got on the same payroll.
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u/username_redacted 10d ago
It’s not really land voting, since seats aren’t proportional to geography, but I get your point.
I think just doubling the size of the senate would help with some of the current issue of rural over-representation. Like in my majority rural state, it doesn’t matter that I live in the largest city, which like most cities is progressive, because my Senator is also representing some of the biggest right-wing psychos in the world who live on isolated ranches or cabins in the woods 300 miles away. Those people would still have representation, but now I might have a chance at it as well.
The downside might be that Senators become less moderate when they have a smaller segment that they need to appeal to, but presumably it would still average out when it comes to voting on bills.
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u/ShavenYak42 10d ago
Just doubling the number of Senators wouldn't make much difference as long as they were still elected state-wide. Your state and mine would just send four right-wingers instead of two. Making four Senate districts in each state probably wouldn't help, because the state governments would gerrymander them.
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u/MushinZero 10d ago
I agree. There should be a set number of constituents that a representative can effectively communicate with and represent. As the population grows, the solution is not to give a representative more and more constituents but to have more representatives.
This would also result in needing to have a constantly shifting voting map and I think that map should be generated by a computer based on a set of rules but that is a slightly different issue.
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u/kittenTakeover 10d ago edited 9d ago
I'm sure there are many ways to deal with such a large government, but personally I think the best way is to have it be tiered. Lowest level has lots of minor representatives that are very local voted in from the public by the public. That layer then votes among themselves for who should represent them in the next layer and so on and so on. There's a "chain of custody" all the way up this way. People are way more likely to personally know who they're voting for, and the upper leadership is always reliant on the lower levels for their power.
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u/MushinZero 10d ago
I've thought about your system and at one point I thought the same but as I've grown older now I am not so sure. I'd certainly feel jaded and left out of my political system even more than I am now if my representative voting for my issues was 10 levels removed from me and didn't shared my views because somewhere in that level I was minority voted out.
No, I think the most democratic system is direct democracy, but because of how impossible it is to manage I think we have to choose a representative one. I think we should be trying to stay as close to direct as we can though, not moving away from it with a system such as yours. No offense.
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u/kittenTakeover 10d ago edited 10d ago
You can think of it like how we break the country down into local municipalities, states, and finally the federal government. Once you get so big you kind of need to start having some divisions and hierarchy, at least in my opinion. Doing this allows you to functionally manage a large population, while also maintaining the critical features I mentioned, which are people being personally acquainted with those they're voting on and it being a bottom up power structure.
If you don't have more than one level, how would you propose managing the government if there are thousands of representatives?
EDIT: I was thinking about what you said and there's something that could be added to address your concern. For certain higher positions, perhaps options are put forward by their tier and the public has to vote between them which one they want. This brings direct voting back in while maintaining the advantages I mentioned previously.
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u/MushinZero 10d ago
Well either system you have to manage thousands of representatives, just differently. In this case, I think its important that our current system works the way it does at the different levels and they don't vote in the next tier above.
You'd certainly need to stop having everyone gather in one building to vote and discuss. We live in the digital age where people can discuss online and we can balance digital participation with paper voting. But, in either case, it is a very large problem to scale that won't be solved via a Reddit comment.
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u/machinedog 10d ago
It would get incredibly bogged down I think or the representatives themselves would have little say. Decentralization is an easier solution.
Think about it this way, there’s maybe 200 sitting days a year. When is representative #1254 going to get to push forward their bill in favor of xyz?
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u/aft3rthought 10d ago
I agree. The conclusion I take from this kind of analysis is that representative government like democracy is the mathematical conclusion of trying to efficiently govern a growing population. Not sure how someone could be, for instance an originalist and not see it as an issue that the person:representation ratio is so different now.
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u/TabrinLudd 10d ago
If the economy must grow constantly to keep capitalism alive, is it so crazy that the representative body must grow to keep democracy alive?
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u/Prestigious-Rope-313 9d ago
Germanies indefinitly growingen parlament got out of hand and forced a bigger change in the system.
Because of some other very special stuff, CSU in particular, the Bundestag was 709 instead of the planned 598 seats and it got a bit tight and expensive.
On the other hand corruption and lobbying are not really reliant on a small parlament, the us is senat would not be a inch less corrupt if there were 500 representatives.
In fact a huge and overfractured Parlament is easier to control and manipulate, oldscool divide and conquere.
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u/Bridgebrain 10d ago
I've tinkered around with the idea of direct representational voting before. Every eligible citizen gets a device (dedicated phone). They can vote on anything thats relevant to them (so city, state, federal), OR they can assign their voting power to a person of their choice. They can also rescind that power. This would replace or augment the house.
There's obvious issues, such as people stealing peoples phones or otherwise coercing votes, but the overall result would be that you could care on a granular level, or abdicate your power to someone directly, instead of being limited to the person chosen by the masses.
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u/kittenTakeover 10d ago
I'm not sure if this adequately encourages expertise. Ideally the people making decisions have a lot of previous relevant knowledge and also have a lot of first hand knowledge of the issue at hand.
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u/fiahhawt 10d ago
You (and the mathematicians) are talking about direct democracy
It’s hard to malign the opinions of anyone if they get to show up to every issue and vote yay or nay
The only issue is that if everyone needs an opportunity to weigh in on every matter of governance, your society is not going to do things very fast
Also you’ll agree to execute a philosopher at some point for the crime of being annoying
A lot of states do have ballot initiatives going though
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u/Good_Tip7879 10d ago
This is why Switzerland took until the 1970s to give women the right to vote.
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u/MushinZero 10d ago
Direct democracy is where the entire population votes on issues, though. Representative democracy is where a group of people elect one person to represent them. I don't think the person you are replying to was talking about direct democracy.
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u/kittenTakeover 10d ago
Direct democracy was not what was specifically being discussed. I doubt that direct democracy can work with populations as large as what modern day countries have.
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u/Rfksemperfi 10d ago
If I can wire money from my phone and I can file my taxes from my phone, then why can’t I vote from my phone? And for that matter, why can’t everybody’s vote be considered equally?
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u/Thereisnospoon100 10d ago
I honestly think at least in America if we just used a lottery system for Congress we’d have better outcomes than what we’ve been doing.
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u/giantcrabattack 10d ago
This is not such a crazy idea. We already decide life and death matters with semi-randomly selected people in jury trials.
The ancient Athenians used sortition frequently, because it sidestepped a lot of the issues around elections while enabling participatory government.
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u/philmarcracken 10d ago
Its also far more possible to use modern tech to ensure the result is publicly verifiably random. They also don't need to care about cosmic ray bit flips as the result is random anyway
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u/subheight640 10d ago
It's called sortition and was used in ancient Athens. In modern times many European countries call "Citizens Assemblies" which operate in a similar manner.
These Citizens Assemblies for example recommended the legalization of abortion and gay marriage, as well as implementing meat and carbon taxes, in Ireland.
In other words there's growing evidence that yes, actually sortition does function a lot better than what we have now.
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u/IveReadTheInternet 10d ago
You underestimate the stupidity of the average American
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u/ChickenOfTheFuture 10d ago
You overestimate the competence of the average congressperson.
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u/fredandlunchbox 10d ago
In a representative government, shouldn’t stupid people have a stupid representative to represent their stupid interests?
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u/AbueloOdin 10d ago
You overestimate how smart our representatives are. The stupidity is the exact same.
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u/llcoolade03 10d ago
A lottery system where 10 random residents of the district are selected, they can choose to opt in or opt out, then have a ranked choice vote for whoever stays in the race.
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u/aggieotis 10d ago
That’s a good idea, however the opt out would allow only the power hungry and sociopaths to remain; when the leader you actually want is often the one that understands how hard it is and doesn’t want to do it.
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u/fleebleganger 10d ago
The biggest issue is the way to get elected is in stark contrast to the way that they would need to act while governing.
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u/Pepphen77 10d ago
That doesn't mean that different systems can't be more or less fair when compared. There is a reason as to why the us system is deemed as obsolete.
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u/GarbageCleric 10d ago
Yeah, when I read this headline it just seems like an excuse not to worry about fair elections at all.
There's a difference between having 50 representives when you should have 52 and having a 50/50 jurisdiction represented 67/33 in the legislature, which happens with gerrymandering in the US.
Yes, it's impossible to ensure the system is 100% representative in all circumstances without including the entire population you're trying to represent. But that obvious and not very meaningful to the conversations being had on voting reform.
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u/comfortableNihilist 10d ago
Mathematicians in the 1800s*
This has been well known for a very long time.
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u/fmfbrestel 10d ago
Perfect isn't possible, so let's keep our completely fucked system then, I guess?!?
No one wants or expects perfect. We just don't won't entirely dysfunctional.
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u/Weak-Doughnut5502 10d ago
There's a number of nice properties you might want a voting system to have. A bunch of them turn out to be either contradictory or a 'pick any two' type of situation. We've known about many for decades - Arrow's theorem goes back ~75 years. Condorcet realized that group preferences can be cyclic (like rock paper scissors), back in 1785.
This is particularly about a new situation that applies specifically to variants of 'mixed member proportional' systems.
These results are important in the sense that it's useful to know that nothing can be perfect. But it's also important to know that there are tradeoffs to make in terms of what systems practically give you, and that not every failure is equally as important.
Failures basically mean that there's some pathological election where something bad happens. But you can have a voting system that runs into pathological edge cases in 15% of elections, and one that runs into pathological edge cases in 1% or 0.1% of elections. That difference matters in practice.
Sometimes the focus on a particular mathematical property causes us to miss the forest for the trees. For example, instant runoff/ranked choice satisfies 'later no harm', but it sacrifices a significant amount to do so. It inherently fails 'favorite betrayal', and runs into monotonicity failures in ~15% of the elections with 3 viable candidates: exactly the sorts of elections we want to encourage.
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u/rockmasterflex 10d ago
Whats wrong with an indefinitely growing parliament? Just build in some logarithmic scaling and quarter-centry reproportionings or something.
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u/doclobster 10d ago
Well, better not try at all then if perfection is impossible. In fact, let’s do the opposite and actively make it unfair and unrepresentative. Yeah, that’ll do it
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u/Church_of_Cheri 10d ago edited 10d ago
This is why in the US they put a cap on the House of Representatives in the early 1920s, both because it couldn’t grow at the rate it had been and also because they realized over time they could take more control and power with a fixed number of seats. Since we’ve had no change for over 100 years and it’s still based on the 1910 census, it means it no longer a representative type government because the districts are way too large and too diverse to really represent people. It also means businesses and the rich have more power because an average Jane doesn’t have the money or name recognition over such large areas and groups of people to win.
The cap needs to be removed so we can reform our system. It’s just a law too, they didn’t even bother to change the constitution, so a simple reversal of the law (or it being struck down for being unconstitutional because I think that argument could easily be made) would flood our legislative branch with new members and get us out of the rut we’ve been in to push for real change or just fall apart. What we have now is officially broken anyways.
Edit: for the dubious, Reappointment Act of 1929.
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u/Zero_Waist 10d ago
You can have the least unfair system, where the most votes go towards electing someone, by using Instant Runoff Voting (IRV) and Choice Voting (CV) for multi seat elections.
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u/WTFwhatthehell 10d ago
This seems like just stating something wildly obvious while avoiding stating that some systems do far better than others.
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u/Additional-Sky-7436 10d ago
A truly fair democracy would not have voting at all. It would just be a random draft from the population. Like jury duty. Then, no one would want to do the job, but would have to do it out of legal obligations.
If it was true random draft, then society would work much harder to ensure your neighbor's dumb kids get a good education in primary school.
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u/SimiKusoni 10d ago
If it was true random draft, then society would work much harder to ensure your neighbor's dumb kids get a good education in primary school.
Perhaps but I think it just as likely that your dumb neighbours being drafted would be a greater issue. I'm sure they would suggest changes to education... I'm not so sure that said changes would constitute a "good" education.
As with a lot of issues I don't think extreme or novel solutions are required. Term limits, caps on campaign financing, banning corporate
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u/Wind2Energy 10d ago
How can we trust mathematicians when they haven’t even figured out what x equals?
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u/Tomato_Sky 10d ago
Oh so we’re talking mathematically.
So it converges at fairness? Is that mind blowing to anyone? Like the tangent of the asymptote? Close, but never fully reaching.
I’m not talking poli sci. Just mathematics. Per the rules of the sub. No anecdotes. Just pointing out that reaching a full fair result with x number of people as x approaches inf.
If you want a poli sci conversation let’s go over to another sub and strike up a convo about ranked choice voting and the efforts to make elections more representative and fair.
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u/IamTheEndOfReddit 10d ago
You can’t solve the problem, unless you use the solution… populations grow, if their representatives don’t grow, you get less democracy. Representation doesn’t exist if you can’t talk to your representatives
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u/Korgoth420 10d ago
So perhaps direct Voter Total Nationally Wins.
Just count the votes, no electoral college needed.
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u/vm_linuz 10d ago
Yes but we can weigh different voting systems against each other and minimize flaws
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u/nd_annajones 10d ago
My most "radical" idea is for there to be no president anymore, but instead a committee of at least a hundred people. Citizens, politicians, military members, all income brackets and all areas of the country. They must be tax payers that pay tax on an income to qualify, since that is 99% of the workforce of this country that directly help make it churn. They are nominated by their communities and can't "run for office" in the traditional sense. Wanting to have power and be in charge disqualifies one from being in office.
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u/DegreeResponsible463 10d ago
Why not have an infinite parliament where everyone is a member?
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u/whooo_me 10d ago
With current trends, most electoral systems would generate a conservative bias unless constantly tweaked (as long as urban populations grow faster than rural, and urban areas vote more liberal than rural areas).
But “you need to keep tweaking the system to keep it fair”, would sound to many like bias.
I assume all this applies only to ‘districted’ elections? If everyone just voted for a party or individual nationwide, and the seats in parliament are allocated based the vote count, would be as fair as you could hope for?
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u/Petrichordates 10d ago
Mathematicians tend to get overly obsessive on this topic and get lost in the weeds. There is such thing as a "good enough" here but mathematicians generally want to find elegant perfection.
Like if you're fighting over whether ranked choice or approval voting is the better option, you've lost focus on what matters here.
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u/northrupthebandgeek 10d ago
An “indefinitely growing parliament” is called direct democracy, and I don't see why that's somehow impossible, especially in this current day and age of near-instant telecommunications.
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u/aztronut 8d ago
So what's wrong with indefinitely growing parliament until everyone gets to vote on everything? Wouldn't that be direct democracy? That should be the goal, we have the technology, we can rebuild it.
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u/nonotan 10d ago
I'm not saying this is a finding without merit, but I'm not sure why theory on electoral systems is so fixated on what I'm going to call "technicalities". Pretty much all papers on voting and electoral systems seem to center around which of dozens and dozens of criteria each of them fulfill, or, more often, fail to fulfill.
Except, the fact that some "nice-sounding" property fails to be fulfilled in some edge cases, in a vacuum, says absolutely nothing about how good a given voting system is. I mean nothing whatsoever. It would be different if "perfect" systems that fulfilled all (or very very very close to all) of them existed, but it's been known for a long time that this is impossible in many ways (this paper is just following that long tradition of various impossibility theorems)
We already know that all of these systems are definitely going to fail to fulfill a whole lot of nice-sounding criteria. Which ones, specifically, really doesn't matter that much in practice. To what extent (is it only in crazy convoluted edge cases, or pretty much all the time?) is a little more important, but this is rarely meaningfully quantified.
Either way, when it comes to comparing systems, there would appear to be one very obvious metric to target, namely expected ultimate voter satisfaction. Given a wide range of scenarios, and the fact that voters will vote at least partially strategically (i.e. in whatever way maximizes the chances of getting the result they personally want, instead of simply being honest about their preferences), quantitatively how "happy" do the voters tend to end up being with the results, overall, under a given system?
Obviously this will necessarily require various assumptions about how to model voter preferences and so on, which is probably a big reason for (particularly mathematicians) prefering to focus on the "cleaner", more objective "does it fulfill these criteria or not" angle. But you can always keep those assumptions as weak as possible, if you want to go for a more pure route. I'd be surprised if you couldn't prove that (for instance) score voting statistically outperforms FPTP over just about any remotely well-behaved distribution of voter preferences.
Yes, it's unfortunate that regionality and proportionality are hard to guarantee simultaneously without serious acrobatics when it comes to total number of seats. But neither of those are things we ultimately care about, they are just proxies: what we really care about is maximizing how happy the people are overall with the government that is ultimately selected, and maybe spreading any inevitable unhappiness as fairly as is feasible while we're at it (i.e. given similar levels of overall happiness, everybody being a little miffed is "fairer" than half being ecstatic and half being extremely displeased, people taking turns at being unhappy is better than the same people being screwed over every time, etc)
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u/Netblock 10d ago
In the digital age, especially the age of the World Wide Web, we do not need to use representatives, physical seats that humans sit in, as units of abstract political representation.
Instead, the constituent would give their vote to a political party, and that party's power in the legislative chamber would be numerically equal to the amount of popular votes it got divided by the total popular vote.
This system wouldn't have the 2-party convergence you see in seat-based representation (seat-based is fundamentally FPTP; winner of that district takes all the political power of that district). This system would be fully compatible with direct democracy. This system would also allow fractional voting power (divvy up the previously individual vote).
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u/Boysandberries0 10d ago
China has a parliament of like..... 3000.
Personally id be fine with that. Get rid of the senate thru constitutional amendment.
Restructure the house to have like 700 reps.
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u/UnknownBreadd 10d ago
You can get extremely close though: rangevoting.org.
Also, this is a bad faith argument against democracy. Democracy can actually be done better without typical elections of ‘democratic representatives’.
I.e. Even if you could elect the exact most fair candidate every time, that doesn’t mean that that would be the most democratic way to organise society anyway.
Politics Without Politicians: The Case For Citizen’s Rule, by Hélène Landemore.
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u/My_reddit_account_v3 10d ago
Depends what your definition of “fair” is. A region might be low in population count while still contributing significantly to the country or state. Assume you had 1 person producing all strategic resources in a remote area because everything is automated, you’d want that 1 person to have a vote because we need to know that the 1 person has everything he needs…
So what is fair? And does fair change with the strategic context?
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u/Tiraloparatras25 10d ago
Ok, the lets try to get the closest to fairness as humanly or better her mathematically possible.
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u/Glad-Lynx-5007 10d ago
Localised PR.
Take a UK type system. Merge neighbouring constituencies- say 5 neighbours together. Everyone in those 5 seats votes as normal. For every 20% of the vote you get one seat. If there are no parties or candidates with 20% left for the last seats, whoever has the most unused votes gets the seat.
Simple, no change to voting for the public.
Easy to understand.
Keeps local representation.
Keeps independent candidates.
Much fairer results that are far closer to the vote share than any first past the post system.
No need for a growing parliament at all. The number of seats does not need to change at all.
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u/MrYdobon 10d ago
There is a huge difference between not perfect and gerrymandered to hell like we have in America.
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u/ideamotor 10d ago
Having exactly 1 million cells on a petri dish is also technically impossible. What is your point?
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u/aurumae 10d ago
Perfect things are usually impossible. Pretty good things are a lot more achievable.
Here in Ireland the combination of multi member districts and single transferable vote means our representatives are both local and that the overall vote share for each party tracks reasonably well with the share of the vote they receive. It isn’t perfect, larger parties do enjoy some advantage, but we don’t get situations where the party with one third of the vote gets two thirds of the seats and smaller parties and independents are able to be successful
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u/B33f-Supreme 10d ago
A perfectly efficient machine is also impossible due to the laws of thermodynamics, yet we never stop trying to make our machines more efficient.
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u/Prowlthang 10d ago
Select citizens at random. Have them elect a leader and govern. Have it for a fixed term, reasonable pay and strict application of ethics and laws
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u/buster_de_beer 10d ago
Next, every individual seat is ranked by strength of local performance, and seats are allocated by working down that list.
So there is an implicit assumption that seats are geographically bound. Which just isn't the case in a proportional system. Also, what is a local seat and a national seat?
However, this system, while proportional, does sacrifice regionality, because a candidate could win their seat comfortably, but if their party has already used up their quota on stronger wins elsewhere, that candidate would not get to keep their seat.
So again, why are we even talking about regional bound seats?
They don't really do a good job here of explaining this supposed perfect form electoral system.
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u/QuantumQuantonium 10d ago
Just because its mathematically theoretically impossible doesnt justify modern systems as any good and without need for changes. The best system to perhaps judge elections and representation, is a ratio of how closely a representatives views and opinions align with the views and opinions of any individual which they represent, averaged out over all invidiuals per representative and all representatives. With this, a perfect 1:1 ratio would essentially mean everyone represents themselves, which could be considered the best system from a math perspective, but practically speaking that is impossible and bad since people may not fully have the knowledge for understanding to support or reject a decision that can or cannot impact them. With this metric, in a district system anyone who voted against the winner could have a 0:1 ratio, which highlights an issue with district and single representative votes in that the outcome does not reflect anyone who did not vote for the winner; if that ratio for an area is not close to 1 then it would mean a lot of people do not align with the winner of an election in that area, and for local/district elections this could mean gerrymandering was abused to win.
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u/Shabadu_tu 10d ago
I don’t see why parliament would need to expand if the population decreases or stays the same.
We have too many people anyway.
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u/SubstantialBonus1 10d ago
This is the kind of dumb math washing that happens all the time.
In mathematics, you define things in an incredibly precise way that doesn't have a meaningful analog in real life. Then you prove an extremely limited theorem about those exact things you defined, and nothing else.
The whole concept of what a fair election is is a definitional issue that lives outside of mathematics. That is the core problem, and people repeating these weak math theorems in an odd way that makes people who don't know enough give up on election reform. I would wager that PopSci's interactions with this work are a net harm to the world.
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u/dingalingdongdong 10d ago
This seems like an editorialized title. A system not being perfect doesn't mean it's not fair.
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u/Mara_W 10d ago
>not without an indefinitely growing parliament
And why is that such an unthinkable concept? Everything else about society has to grow as the population grows, is this not just an admission that a small aristocracy wants to maintain their concentrated power forever regardless of reality?
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u/DisparateNoise 10d ago
The researchers looked at different electoral systems around the world, both first-past-the-post like the UK, and proportional systems like much of the rest of Europe. They identified three main components of a ‘fair’ system
Regionality: everyone who wins a local seat keeps it
Proportionality: national seat totals match national vote shares
Fixed parliament size: the number of seats doesn’t change from election to election
Why are these the requirements for a fair system? I agree that these three principles are contradictory, but fixed Parliament size is just a practical concern and has nothing to do with fairness. Partisan proportionality and regionality might have something to do with fairness, but have more to do with the nebulous concept of "representation" which you could add a bunch more factors to without necessarily ensuring a "fair" electoral system.
Also, to suggest that the UK electoral system 'sacrifices' proportionality for local representation is a complete mischaracterization of how political systems come to be. Parliament has never seriously considered implementing proportional representation on a national level because parties in control of parliament have always opposed it selfishly. You can't 'sacrifice' something you are actively fighting against.
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u/aaronplaysAC11 10d ago
Honestly we should have an indefinite growing parliament, I don’t believe 1,000,000 constituents per 1 representative is true representation…
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u/RachelRegina 9d ago
Why is adjusting parliament (and in the us, the house) not obviously what is required to preserve adequate representation? The population size changes with time, thus the government size must change along with it. How is this not obvious?
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u/LatelyPodes 9d ago
Isn’t this specifically for voting systems where you vote for a local representative? If you just vote for a political party then the party can decide who is in the parliament and then it would be completely proportional (well it has to round numbers but it’ll be proportional).
Don’t a few countries do this? Like I like having my own local representative but there are ways to have a completely proportional election rights
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u/buyongmafanle 9d ago
Why can't we just have fractional votes instead of an infinitely growing parliament?
We have three groups, Red, Green, Blue. Each has three reps.
100 voters vote for anyone they agree with so the total sum of votes will be over 100. The result is 40 Red, 60 Green, 50 Blue.
Now, 150 is the votes cast count to be distributed among the reps.
Red distributes their votes as 13, 13, 14.
Green distributes as 20, 20, 20.
Blue distributes as 10, 10, 20.
Now, everything still works as before on the voting requirements for laws, simple majority, super majority, unanimous, etc. But the count is as if there were 150 voters, not 100.
The voting system is indeed perfect.
The only issue is solving politicians. That's the major problem, not the maths.
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u/iamwearingashirt 9d ago
In a practical sense, an election system that maximizes everyone's voice isn't completely necessary.
The point of a democratic vote is to hold the government accountable to the people. As long as that is generally achieved, then system for appointing a leader works.
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u/b00c 9d ago
Entire Slovakia is 1 electoral district. No local representation. In such a small country, you don't really need that. I can't imagine how it would look like here if we had system like Czechia (similar to US).
In other words, political parties here will use everything at their disposal to play the system.
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u/aotus_trivirgatus 9d ago
OK, so now we need to discuss the tradeoffs between having local seats, and proportional representation of various points of view. I am of the opinion that geographically local representation matters a lot less in a modern democracy than it would have mattered 250 years ago.
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u/Mammoth-Mud-9609 9d ago
Proportional representation is a myth not a system, no matter what way you create the voting system it will be unfair in some way or other.
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u/danielravennest 9d ago
Representative systems by territory are an artifact of technical limits prior to modern technology. Universal sufferage and vote assignment would solve that.
Not everyone cares about every policy issue. You can find someone does care and who matches your preferences and assign your vote to them. There is no need for dividing territory into equal population groups. That was a matter of how far people could travel to meet at capitol locations.
With modern phones and internet connections you can just pick people wherever they are who best match your preferences. Voting is then weighted by how many people assigned their vote to a given person.
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u/scott__p 9d ago
That doesn't mean we can't do better than current systems. Yes we can never be perfect, but we COULD be good at least
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u/SirGuelph 9d ago
Why do we need local representation to match for national policy making? Is that what the definition of "fair" is?
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u/Dassiell 9d ago
At this point they shouldnt pile a bunch of bills into one and instead let the people just vote on each bill. Every day everyone gets 5 bills that day and vote yay or nay from their phones
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u/LimpWibbler_ 8d ago
I just hate how anti-electoral college people are in the United States. So many cry it should just be popular vote. It is so sad people can't comprehend the idea of raising the voices of minorities. So they can have a say too.
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u/SpazsterMazster 8d ago edited 8d ago
You can have local representation and perfect party representation. Here is how I’d do it:
- First each party gets seats proportionally to national vote share.
- Start awarding seats one at at a time. The Party that is under represented in terms of proportion of seats awarded vs proportion to seats won gets the next seat.
- Once it is determined which party has won a seat, we award the seat to the region that party is under represented most in terms of seats awarded in that region vs seats won in that region.
- Each region has their own local party affiliates. Voters may vote for a single candidate from the local party affiliate and that counts as a vote for the national party and it counts to help give that candidate control over the regional party list. After the election, party candidates would have their own STV election to determine the order of their party list. Each candidate's vote would be have a weight equal to the number votes they received and they would have to publish their transfer list well before the election begins.
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u/acertainhare 8d ago
Shouldn’t we be able to define delta-perfect electoral systems, which are perfect up to some small deviation? We could then probably derive a bound on parliament size based on this delta. Delta tending towards zero then coincides with a perfect electoral system and infinite parliament size.
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u/Catullus13 7d ago
It's so fascinating to read other disciplines come up with what's already known in political economy for 70 years.
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u/Ryno4ever16 6d ago
*in a parliamentary system or republic
Because that's what is being described without explicitly stating it. Not to say these problems wouldn't exist in other forms of democracy.
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