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Voting-like mechanisms which address size of preferences?

by abramdemski7 min read18th Mar 202130 comments

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Voting Theory
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First, a few motivating scenarios.

1: Legislative Deadlock

A legislature consists of a split two-party system, with 50 Morlocks and 50 Eloi.

Morlocks run all the machinery which produces important goods such as clothing. They really want worker rights, such as vacation time, air conditioning, etc. Also, they enjoy eating Eloi.

Eloi really want to pass an anti-cannibalism bill. They are also mildly against passing the Morlock worker-rights bill.

For the sake of argument, let's say the Morlocks get +10 utility from worker rights, and -1 utility from the anti-cannabilism bill. Symmetrically, the Eloi get +10 from anti-cannibalism and -1 from worker rights.

If the two bills are considered separately, neither will succeed, because both only get 50% of the vote. (I'm assuming for the sake of argument that a tie is not sufficient to pass a bill.)

If the two bills were bundled together, and the legislators vote myopically (considering only the pros/cons of the bill set before them), then we can achieve the best case scenario: both measures get passed, for +9 to both sides.

However, both the Morlocks and Eloi would prefer to pass their bills without the "pork" of the other bill tacked on. Plausibly, both parties will coordinate to make sure the bills are only ever introduced separately, or vote against the combined bill when it is introduced. Instead, they'll each attempt to bully the other side into lesser concessions. This is especially true if the two parties hate each other; voting in favor of worker rights for Morlocks may be seen as a "betrayal" of the Eloi base, and vice versa.

From this, I draw several lessons:

A. Tit-for-tat in the legislator is not automatically bad. Before thinking about this scenario, I was thinking that deals like "I'll vote for your bill if and only if you vote for mine" were a problem, because they distort the vote (I was thinking that it's best if everyone votes honestly). But if the two bills are voted on one at a time, we want 1 Morlock and 1 Eloi to make a secret deal to vote on each other's bills! Then both measures would pass.

B. Legislation is, importantly, an iterated game rather than a series of single-shot votes. This has pros and cons. On the pro side, tit-for-tat voting strategies can improve overall outcomes. On the con side, tit-for-tat can end up in deadlock where everyone hates everyone else and won't pass each other's bills, due to perceived wrongs in the past.

C. Legislation is combinatorial. One bill isn't really one bill; it will typically contain a complicated combination of policies. Passing one bill at a time is basically navigating a complicated multidimensional space via binary decisions. But how we organize the complicated space into binary decisions will make a huge difference in how the legislature navigates it.

2: Oversized Minority Influence

Now consider a scenario where we add one more legislator, the Time Traveler. The Time Traveler is an independent, not a Morlock or an Eloi.

The Time Traveler can break the deadlock between the Eloi and the Morlocks by voting "yes" to both bills. However, the Time Traveler is a radical who wants something in return. Specifically, the Time Traveler wants to restore the human race to what it once was through forced interbreeding of Eloi and Morlocks, destroying the Eloi/Morlock society as it currently exists.

One radical legislator should realistically be ignored or almost ignored. Instead, the minority now has a huge influence on proceedings, because he can ask for something in exchange for his vote.

3: Undersized Minority Influence

What if the Time Traveler sides with the Eloi, instead? Now, we have 51 Eloi and 50 Morlocks. So long as they can maintain party unity, the Eloi can pass whatever they want. This doesn't seem right!

Proposals

1: Voting currency

Each legislative term, each legislator starts with one thousand votes. They can use these votes however they want; they might blow all 1K votes on a single big important issue, or use just one vote on each issue, or whatever. This allows strength-of-preference to be expressed, which hopefully helps pass both bills.

This stops undersized minority influence: the minority is no longer helpless. The Morlocks can let the Eloi pass their no-cannabilism bill, saving their votes. Then, they can pass their own worker-rights bill with the votes they saved up. The Eloi can't oppose the bill because (hopefully) they used up too many votes getting their own bill.

This sort of codifies tit-for-tat into a mechanism. Spending more voting power now means less later. So if an Eloi spends one more vote now, the Morlocks have 1 more vote's worth of advantage later.

Variations: the winning group might "pay" the losing group, splitting up the winning votes between the losers. Also, legislators might get a "vote allowance", perhaps getting +10 votes per week rather than getting them all in a lump sum at the beginning.

Objection #1: legislative flip-flop.

The parties could go back and forth in power, based on who has the most votes left. First, the Eloi pass a bill banning cannibalism, exhausting half their vote supply. Then, the Morlocks use their new pseudo-majority to pass a bill which makes cannibalism legal again and establishes worker rights. However, they exhaust most of their votes in doing so, allowing the Eloi to pass a bill which makes cannibalism illegal again, and rescinds worker rights. Etc. This process could terminate when everyone runs out of votes, but it's still pretty bad.

A proposed solution: bills cannot be contradicted by bills which pass with less votes. The Eloi bill might pass initially with 25K votes from the Eloi. (Remember, the Eloi have 51K votes total, due to the Time Traveler siding with them.) Then the Morlocks would collectively need to spend half their votes to overturn it. But they don't need to: they can just pass their own bill.

The strategy here is complex. The Eloi could put a clause in their bill making worker rights illegal, so that the Morlocks do have to overturn the Eloi bill in order to pass worker rights. But then the Eloi could expect their bill to be overturned, so they'd have to spend more than 50K votes to pass it, to cement it in place. But spending this many votes gives up a lot of power.

Objection #2: strategic bills exhaust the other party

I think the critical flaw with the vote-currency idea is that someone can introduce red-herring bills which the other party has to vote down, but which stand no realistic chance of passing in the first place. This exhausts the other party's votes, increasing your party's power "for free".

For example, the Morlocks might repeatedly introduce the Food Bill, under which all Eloi would be immediately exterminated for food. The Eloi don't know exactly how many votes the Morlocks will cast, so to make sure they don't get eaten, they have to spend a good number of votes against this. Eventually, the Eloi's votes will be exhausted, and the Morlocks will be free to do what they like.

Together with example #1, this shows that the power to decide which bills get voted on, and in which order, is critical. Whoever controls this can significantly manipulate the outcomes. Perhaps this should be a significant aspect of the mechanism design? (I won't introduce any proposals for how to handle this, but, I welcome them in the comments/answers.)

2: Quadratic Voting

This is the same as the previous suggestion, but rather than "votes", you get "voting money". Votes are purchased with a quadratic formula, such as:

Amount SpentVotes Purchased
11
22
43
74
115
etc.

Roughly, this encourages you to spread out your votes rather than blow everything on a few bills, because purchasing votes for the same bill gets increasingly expensive.

More precisely, the hope behind quadratic voting is that voters will buy votes proportionate to how much they care about an issue. If this were true, it would provide a nice guarantee of utilitarian outcomes. For example, in legislative deadlock scenario, we would hope that Morlocks would cast 10x as many votes in favor of working rights as they would cast against the anti-cannibalism bill; and similarly, Eloi would be willing to cast 10x as many votes in favor of anti-cannibalism as they would against worker rights. Everybody wins.

Unfortunately, this seems far from true.

Objection #1: Quadratic voting discourages voting on losing propositions.

The idea that quadratic voting incentivises you to vote proportionately to your preferences is based on the idea that the derivative of the quadratic formula is linear, so the cost of one additional vote is proportional to the number of votes you've already purchased. (In the example table above, the cost of one additional vote is precisely the number of votes you've already purchased.) This means if you stop when cost=benefit, your number of votes represents the amount of benefit.

The problem with this argument is that the benefit of one additional vote is based on the chance that it tips the election in your favor. So we shouldn't expect your votes to be proportional to the utility of a given option. Rather, we should expect your votes to be proportional to utility times probability

This means that quadratic voting, like plurality voting, has a high incentive to avoid voting on losing propositions.

This doesn't create an obvious problem in the Morlock vs Eloi examples, but it can create big problems in general. 

For example, suppose the legislature has to elect a Prime Minister from amongst its members. Traditionally, Morlocks vote for the current head of the Morlock party, and Eloi vote for the current head of the Eloi party, and one of the two wins by a narrow margin. Everyone knows it's a waste of votes to consider anyone else, purely because everyone knows it's a waste of votes to consider anyone else. (A lot like presidential elections in the USA.)

That's bad enough -- it would be better if they could elect the moderates to Prime Minister, but it's impossible (because everyone knows it's impossible, so no one would bother to vote that way, so it's impossible in fact).

But now suppose there are two Time Travelers. Both Time Travelers are worse for everyone than the Morlock or Eloi party leaders. However, there's a huge amount of buzz about the Time Travelers, because they're new players. No one knows whether they're feasible candidates or not. There's a lot of discussion of the pros and cons of the two Time Traveler candidates. The Eloi suspect the Morlocks will vote Time Traveler just to spite them, and vice versa. In the end, one of the Time Travelers gets elected, because everyone is afraid their least favorite Time Traveler will get elected and so votes for the other; and the Time Travelers have the advantage of being able to get votes from both sides, rather than only one like the Eloi and Morlock candidates.

Note that this can be an equilibrium: if everyone knew the race would come down to one of the two time travelers, they wouldn't want to waste any of their votes on the more traditional candidates, even if those candidates are better in every way.

So quadratic voting can produce perverse equilibria much like we see in US elections, where few really like the candidates they vote for.

Objection #2: We still have the problems from before!

In addition to this, we still have the problems from the previous proposal, IE the legislative flip-flop problem and the exploit where you introduce "troll" bills to get the other party to use up its votes. These are pretty bad problems!

3: Nash Voting

An earlier post of mine attempted to quantify the "strength of preferences" idea not by considering how much you're willing to spend votes on the current issue vs save up for the next one (which is the primary mechanism I'm considering here), but rather, by trying to quantify voter's "zero points", AKA their "BATNA" / "threat point". Basically, this quantifies how much you care about the current issue by comparing it to open revolt, ie defecting from the government. If someone is close to preferring open revolt, this means they're not getting a fair deal under the current system and their preferences should be weighted more heavily.

This has some nice theory associated with it, but the concrete proposal is not any good at all. For one thing, I provided no incentive to honestly report the BATNA. Everyone should set their BATNA high in order to make their preferences louder.

However, I haven't totally lost hope for the idea, so I wanted to mention it. Any ideas for a realistic voting procedure that takes BATNAs into account?

Questions

  1. Any ideas for iterated voting theory, ie, voting theory which takes into account the iterated game rather than pretending each vote is its own isolated strategic game?
  2. Any proposals for a mechanism like quadratic voting, IE which gets people to vote proportional to their preferences, but which lacks the bad-equilibria problem?
  3. Any proposal for a mechanism similar to quadratic voting or my simpler voting-points proposal, IE which lets you transfer votes to issues you care about rather than one-vote-per-issue, but which lacks the fake-issue exploit where you can drain opponents of their votes?
  4. Can anyone propose a better version of my anti-flip-flop mechanism, ie, you need to pass something with greater-or-equal votes in order to contradict previous legislation?
  5. Any better analysis of when tit-for-tat voting is good or bad for the people overall, and mechanisms to prevent/facilitate it to get better outcomes?
  6. Similarly, any analysis of when putting "pork" (ie extra stuff) into a bill is good/bad? It's generally thought of as bad, but my motivating examples make it look good. We want the anti-cannabilism bill to have worker-rights "pork" added in.
  7. Relatedly, mechanisms for avoiding/encouraging pork?
  8. Any proposals for splitting up the task of introducing bills vs voting on bills, so that the legislature can't play games with which version of a bill gets introduced or which order things get voted on? How should we design a mechanism for introducing bills? Should someone else than the legislators do it?

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7 Answers

Ralph Merkle's Dao Democracy addresses size of preferences because constituents only  "vote" by reporting their own overall happiness level. Everything else is handled by conditional prediction markets (like in futarchy) to maximize future happiness of the constituents. This means that if some issue is very important to a voter, it will have a greater impact on their reported happiness, which will have a greater impact on what proposals get passed.

Using Futarchy is just cheating ;3

But you're right, this does negate all my issues. I was just looking for something closer to existing governments.

I suspect the problem is unsolvable, as long as there is private information about preferences and beliefs.  Even the relatively strong weighting mechanisms of https://en.wikipedia.org/wiki/Futarchy ( conditional prediction betting, where correct predictions get promoted because they pay out ) are very susceptible to adversarial choice of proposals to vote on.  

Some systems can be strategy-proofed to elicit true beliefs on a few chosen topics, but whoever chooses the topics is going to have oversized influence in how it plays out.  Quadratic systems (and any directed-vote mechanism) can be EASILY gamed by aggregating decisions into a bunch of small, independent issues that one group prefers, and a few large bundles that another prefers.  In wargaming, we'd call this "soaking off" the damage - letting the opposition waste their votes on less-important things.

 

Another solution to "Objection 1: Quadratic voting discourages voting on losing propositions" is the idea that only the winners of a quadratic vote actually pay an average of the tokens, and everyone else gets a refund - sort of like a blind Dutch auction of the decision.

For example, a quadratic vote is taken between two binary options A and B. A receives 400 votes, B receives 500. B wins the vote, so an average of 450 is taken from the voting token pool of B and 50 tokens are redistributed equally amongst B. Everyone who voted for A gets a full refund.

Consider in your example of selecting a head of state. If a political party overextend their voting to elect their guy - that is, that they overvalue the position - then they will be punished by a lack of voting tokens compared to the opposition for other cabinet positions.

Wait, so, my previous analysis doesn't make that much sense. I now think your claim is pretty plausible.

Expected value if you don't buy one more vote: 

Expected value if you do: 

Here,  is specifically the probability that candidate  ends up in a tie without our one additional vole. I'm assuming the vote uses the (rather dumb) tie-break procedure of choosing randomly from all the candidates, for simplicity. Hence, breaking the tie steals probability equally from each candidate (including... (read more)

1sxae18dI'd be lying if I claimed to fully grok the maths, but I'm glad it was a useful suggestion!
2abramdemski13dHm, I just noticed that I didn't really get your whole proposal in the first place -- I latched onto "full refund for losing positions", but ignored the rest. What's supposed to be going on here? You seem to be ignoring the quadratic formula -- an individual must spend v2tokens to purchase v votes on a candidate. Thus the number of tokens total spend on a candidate isn't a simple function of the number of votes on that candidate; it also depends on the distribution of votes among voters. So the concept of "redistributing equally" gets kind of complicated. If it's supposed to be like a Dutch auction, maybe the idea is that we look at the total number of votes needed to win, and we refund votes (starting with most expensive and going down) until we reach the number needed to win, at which point we stop refunding. This way people don't need to worry too much about overpaying for success. I don't know if that's good or bad, though. Anyway, I'm curious where you got the idea. What made this suggestion natural to you? I'm personally not that familiar with the literature on Quadratic Voting, so as far as I know, this is a standard suggestion. Or maybe it seemed natural to you based on familiarity with auctions?
1sxae12dAh yes, you're right in redistributing the 50 tokens when refunding the winners in the same proportion is tricky. Probably necessitates being able to have fractional tokens so you can refund someone 0.1 token or something like that. I imagine it will be very simple for the losing choices. Also, I don't mean a regular Dutch auction, I mean a blind one where all bidders submit their bid at once (like an election). My understanding of a blind Dutch auction is that it resolves this "people don't bid because they don't think they could win" result in general auctions. This was absolutely an intuitive suggestion from reading about voting theory and auctions, you've got a much deeper understanding of the VT maths than I do. I do think that thinking about elections like an auction for a decision can be a useful way of thinking about it, but I don't have professional experience with this beyond helping to design some videogame economies. Don't take this as any kind of standard suggestion - just mine :)

Oooh, is it really that simple?

Expected state of affairs if I don't buy one more vote (ignoring what else I could have done with the money):

, where  is the probability of candidate  winning if I do nothing, and  is the utility of candidate  winning.

Expectation if I do buy one more vote:

, where  is the candidate under consideration,  is the probability there would have been a tie w/o this one extra vote, and  is the utility adjustment for losin... (read more)

1sxae20dI'm surprised that we are looking forPxto disappear entirely, I'm not sure I understand that. Quadratic voting shines when you have lots of votes with the same voting token pool, because you force people to allocate resources to decisions they really care about. It's absolutely not meant to decide one decision - it's meant to force people to allocate limited resources over a long period, and by doing so reveal their true valuation of those decisions. I would therefore fully expectPxto play a part in every agent's considerations, as they must consider the probability of success in each vote in order to plan allocation of voting tokens for every other vote.
2abramdemski18dInteresting. But then how do you argue that it gives approximately correct results? As I understand it, Weyl sees the argument as just: votes end up being roughly proportional to utility (under a lot of differenc scenarios/assumptions). When this condition holds, the quadratic vote is a good representation of the utilitarian value of the different options. So, the reason I think we're looking forPxto disappear entirely is becausePxis a function ofx! It's fine ifc=α+γUx−√ζBB(7)or whatever, so long as none of those extra terms are a function ofx, so that in the endcis still proportional to (some normalization of)Ux. You're effectively arguing that it's OK to divide byPx+ϵ, because this just represents voters rationally investing less in cases wherePxwill probably win anyway. But this means the quadratic vote systematically undervalues the candidates who are seen as the probable winners! OK, but this should mean the quantity we are willing to spend on an election is overall adjusted up or down based on properties of that particular election (IE, how much the issue matters to us). This should not mean a dependence onPx; a dependence onPxdistorts the vote, compromising it as a representation of collective utility.
1sxae18dInteresting, you make some great points here and I don't think I have any good refutations to any of them. Perhaps if we play around with the auction structure by which we take away and refund these tokens?

An election system which encourages many relatively small parties getting seats

In systems where many small parties need to form a coalition in order to create a government, something like this happens organically. Since no party can get enough seats to pass a decision just by their own votes, they need to bargain with other parties: in the upcoming year, we will support your position X which is unimportant to us, in exchange to you supporting position Y that we care about. 

The amount of demands that a party may require is roughly proportional to their size - if you got 60/200 seats and are bargaining for coalition membership, you can insist getting more things your way than the party that got 10/200 seats can - but it also means that a small party whose voters care really strongly about a particular issue can swing things their way by bartering themselves support on that issue in exchange for collaborating on everything else. 

For example, the Swedish People's Party of Finland was part of every government formed in Finland between 1979 and 2015 despite hovering around only 10/200 seats in each election, because their primary agenda was protecting the position of Swedish as Finland's second official language and being willing to cooperate on almost anything else in exchange. (They got kicked out after the 2015 elections, when the right-wing True Finns party got lots of seats and didn't want to collaborate with the filthy Swedish-speakers. But then after the 2019 elections, the SPPF was in government again.)

Interesting, thanks!

A big part of the motivation for this question was that I've had a longstanding anti-two-party stance, due to the apparent dysfunction of two-party politics in America. But I was talking with some people about it recently, who were of the opinion that many-party systems in other countries were not much more sane/effective. This got me thinking about ways in which my ideal could be compromised. Although my question mainly talked about a two-party scenario, the real motivation was to "avoid shenanigans" more generally.

The time-traveler ex... (read more)

2Kaj_Sotala13dMostly, I think, voting systems designed to ensure that parties get a share of seats that's proportional to their number of votes ("party-list proportional representation [https://en.wikipedia.org/wiki/Party-list_proportional_representation]" is what Wikipedia calls it). E.g. the D'Hondt method [https://en.wikipedia.org/wiki/D%27Hondt_method] seems pretty popular (and is used in Finland as well as several other countries). As for whether it's actually better overall - well, I grew up with it and am used to it so I prefer it over something that would produce a two-party system. ;) But I don't have any very strong facts to present over which system is actually best.

There's a second issue here.  Any 'voting system to accurately measure preferences' is in the class of systems trying to exact information from voters.

The fundamental issue is that individuals can be brilliant, the average of a large population does very poorly on any sort of measurement of how much information an individual can supply.

That is, you are trying to extract (oversight for a complex system) from a pool where (almost everyone is unqualified and doesn't know anything useful).  

I agree that preferences is something you would like to extract, but how can you even show that [a given politician acted to maximize those preferences] or [a proposed policy was even the one with the highest expected value against the consensus preferences].  Similarly, voters are bombarded with [outright lies as to the actual consequences of a proposed policy] and [outright lies about ground true reality]. 

The "what do you know and how do you know it" rationality question to me tells me that voters aren't contributing much information.  (in today's 2 party system at most you get 1 bit per voter, not enough to run a government.  Your proposal you are getting maybe 4 bits per voter)

I theorize that the actual reason democracy 'works' is because the actual information to run a government is coming from elites, just that instead of a single unaccountable elite (a dictatorship), voters can express preferences to stop the absolute worst behaviors by the elite.  (except, uh, all the times they fail to do this)

And, like above, an elite has to get voters to vote for a policy by [convincing voters that it's in their best interest, a children for food policy would be difficult to pass] and [spending money on such persuasion].  Since elites that are more successful have more money to spend, and [success is correlated with competence], then this system is extracting information from a pool of [statically probable to be competent] elite and this is why it works at all.

You can also predict failures.  For policies where [most elite will not live to see benefits], they are unlikely to be supported.  For example, most elites will be dead when climate change is predicted to get really bad.  For things where the elites benefit but the average voters don't, like tax and union and immigration and criminal justice policies, it comes out in favor of elites...

I theorize that the actual reason democracy 'works' is because the actual information to run a government is coming from elites, just that instead of a single unaccountable elite (a dictatorship), voters can express preferences to stop the absolute worst behaviors by the elite.  (except, uh, all the times they fail to do this)

This was my background assumption. That's why I kept the examples to legislators instead of postulating a voting public. I'm assuming you want to elect legislators rather than solve everything with direct democracy.

And I agree th... (read more)

If both parties would prefer [both provisions passed] to [neither provision passed], wouldn't the incentive be to propose a combined bill with both provisions?

Agreed. I guess I'm trying to illustrate a couple of things:

  1. How things are sequenced as bills matters a whole lot. The bills presented individually would fail (unless people engage in tit-for-tat), but the combined bill would succeed. It would be much better if we had a guarantee that any sequence of bills would be voted on just as if it were the best combined bill (where "best" means something like utilitarian-best).
  2. Tit-for-tat can save the day in this example, but the "dark side" of tit-for-tat is when we get in defection spirals. In that case, a combined bill might be politically infeasible. This seems like a realistic model. The two parties can be angry enough with each other that they can't cooperate.

My suggested solution is to simulate a pure issue democracy as closely as possible. Hopefully less than 50% of the total population is in favor of cannibalism, so that provision won't pass. And maybe more than 50% is in favor of worker rights, so that does pass.

This seems to just be rejecting my hypothetical.

I can construct a similar dilemma where there's three single-issue parties, and each one really wants their pet bill passed, and slightly dislikes the other two bills. Would you have them pass none of the bills (the worst outcome in my view)?

8 comments, sorted by Highlighting new comments since Today at 9:08 PM

Very interesting - I'll give some thought to answers, but for now a quick cached-thought comment:

A proposed solution: bills cannot be contradicted by bills which pass with less votes.

I don't think this is practical as a full solution to this problem, since a bill doesn't need to explicitly contradict a previous bill in order to make the previous one irrelevant.

You've made foobles legal? We'll require fooble licenses costing two years' training and a million dollars.
You've banned smarbling? We'll switch all resources from anti-smarbling enforcement to crack down on unlicensed foobles.

Of course you could craft the fooble/smarbling laws to avoid these pitfalls, but there's more than one way to smarble a fooble.

You've made foobles legal? We'll require fooble licenses costing two years' training and a million dollars.
You've banned smarbling? We'll switch all resources from anti-smarbling enforcement to crack down on unlicensed foobles.

Agreed. But it's not a totally meaningless rule. The fooble-legalization bill could include language preventing any restrictions on fooble use and possession, such as licensing. As for Smarbling, the budget for anti-smarbling enforcement will have itself passed with some margin, which you'll have to surpass to repeal the funding.

Funding is itself a huge issue, though. I'm pretty tempted to say that the budget just shouldn't be passed as a bill in the same way.

Proposal 1: Average Budget

Each legislator draws up a budget, and the total budget is just the average of all of these.

  • Objection: strategic budgeting
    • If I know how everyone else is going to budget, I can make the end budget turn out any way I like by putting sufficiently large numbers on my proposal. 

Proposal 2: Allocated Budget

Each legislator gets their share of the federal budget, which they can spend however they like.

  • Objection: too little accountability?
    • It seems like politicians would spend too much of the money on their own projects, potentially in corrupt ways, since they wouldn't need to get it approved by others. In theory, this behavior would get them voted out of office; but if everyone was doing it, it might be difficult for voters to find replacements who would behave better.
  • Objection: how to decide total budget?
    • This requires some other method.

Proposal 3: Quadratic Funding

Each legislator gets points which they put toward budget items (out of a list of budget items any legislator can add to). Then the total amount spent on a budget item is proportional to the square of the sum of the square roots of the number of points allocated to that item by individual legislators.

I don't know this much about this option, but it seems potentially pretty good.

Objection to the whole project: a budget item might have pretty nonlinear returns on money, EG be worth nothing if it doesn't get at least a billion dollars in funding. An approach like averaging or quadratic funding could end up unexpectedly allocating a highly inefficient amount, like just shy of a billion dollars.

Combinatorial Voting

Moving beyond budget, back to the general project:

Budgets are just an extreme example of the general point, that bills are multidimensional objects. Forcing things into a bunch of individual yes/no votes makes things artificially simple, and ends up highly distorting the voter preferences.

Far better if we can vote directly on combinatorial issues. But that's a tough issue.

Controlling what gets voted on, and in which order, is a significant feature of any voting body/process. The common decision across environments seems to be that the faction or coalition that can command a majority gets to set the agenda unilaterally (or via back-room conversation based decision making between coalition partners)

It would seem better if, at least, the agenda were set by the most moderate person.

For example, the lawmaking body could elect the agenda-setter via 3-2-1 voting or STAR voting or some other sensible many-choice single-winner election method, with all lawmakers being candidates on the ballot. The winner of this process would probably be more moderate than the typical winning-coalition leader.

The theory is that this one person is most representative of the governed, and should cleverly optimize the agenda to minimize distortion.

Objection #1: Quadratic voting discourages voting on losing propositions.
The idea that quadratic voting incentivises you to vote proportionately to your preferences is based on the idea that the derivative of the quadratic formula is linear, so the cost of one additional vote is proportional to the number of votes you've already purchased. (In the example table above, the cost of one additional vote is precisely the number of votes you've already purchased.) This means if you stop when cost=benefit, your number of votes represents the amount of benefit.
The problem with this argument is that the benefit of one additional vote is based on the chance that it tips the election in your favor. So we shouldn't expect your votes to be proportional to the utility of a given option. Rather, we should expect your votes to be proportional to utility times probability
This means that quadratic voting, like plurality voting, has a high incentive to avoid voting on losing propositions.

I think the point of quadratic voting was as follows:

Each legislative term, each legislator starts with one thousand votes. They can use these votes however they want; they might blow all 1K votes on a single big important issue, or use just one vote on each issue, or whatever. This allows strength-of-preference to be expressed, which hopefully helps pass both bills.

The legislature has a set of ideas to vote on. a) How are they prioritized, or b) What passes and what fails?

If everyone blows 1K votes on a handful of issues, then another round of voting may be needed, with another set of 1K votes, and it's a bit of a mess. Quadratic voting is supposed to even out the distribution - everyone's time is wasted if there are more rounds of voting required.*


This post also worried about issues still existing, while not performing calculations, which might have revealed whether quadratic voting made things worse, better, etc.

For example, by decreasing votes for things desired, does it increase the risk of these 'What if they vote for the time travelers?' effects dominating, or decrease it because things both sides care about are more important to get a little bit of votes on to show preference ordering, and they don't have so many votes to spare on time travelers just to mess with the other side (because sort(100) is 10, maybe it's harder to mess with things).


(*The radicalxchange website may have had an article on this, or maybe it was a news article about its use in practice, but they've since had a redesign, so, I haven't found it.)

This post also worried about issues still existing, while not performing calculations, which might have revealed whether quadratic voting made things worse, better, etc.

Agreed, but, calculations are difficult. Also, the issues seem severe. I think all the options I've mentioned here are probably significantly worse than business as usual.

My first instinct is to be sceptical that it's possible to find enduring compromise and a working legislative process in a society that's split 50/50 between two factions who hate each other and have diametrically opposed preferences.

I suspect the existence of some kind of common ground (mutual interests and mutual trust, at least to the extent of neither wanting to literally cannibalise or exterminate the other) might be a necessary component for avoiding a war between them.

I originally wrote this with an example of farmers vs fishers, where the two groups had some different legislative preferences, but the example just didn't have strong internal logic (I didn't come up with very plausible differences of opinion for the two groups).

The important thing is the payoff matrix. Clearly the two groups have a mutually beneficial agreement which they could reach, if they would look past their animosity.