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...
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...
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...
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...
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:
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)?
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.
Each legislator draws up a budget, and the total budget is just the average of all of these.
Each legislator gets their share of the federal budget, which they can spend however they like.
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.
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.
First, a few motivating scenarios.
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.
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.
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!
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.
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.
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.)
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 Spent | Votes Purchased |
| 1 | 1 |
| 2 | 2 |
| 4 | 3 |
| 7 | 4 |
| 11 | 5 |
| 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.
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.
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!
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?