Storable Votes with a Pay as you win mechanism: a contribution for institutional design
I joined the EA Forum in 2022, with a post describing my interests and agenda. I also declared in my first comment that in my view, among the main existential risk bottlenecks for this Dangerous Century, a critical one is institutional stagnation. E.O Wilson famously said: “The real problem of humanity is the following: we have Paleolithic emotions, medieval institutions, and god-like technology”.
Regarding the Paleolithic emotions, and godlike technology I have nothing to contribute, but regarding the medieval institutions I think I can make some modest contributions.
Here are two of them, very likely my most important scientific contributions so far: the first is an already published journal article, the second, a new pre-print (please, feel free to make suggestions for improvement).
Storable Votes with a Pay as You Win mechanism
This article (“Storable Votes with a Pay as You Win mechanism” [Journal of Economic Interaction and Coordination, pre-print here for access after the expiry of ShareLink]) presents a dynamic voting mechanism on multiple alternatives (Storable Votes-Pay as You Win [SV-PAYW]).
At the beginning, all agents are given an equal number of (infinitely divisible) storable votes. The agents say how many votes they are willing “to pay” for each of the possible alternatives and the most voted alternative wins the election. Then, the votes that have been committed to the winning alternative are deducted from each player’s account, and are equally redistributed among all participants, and a new voting period begins.
The system reduces the incentives for strategic voting: agents do not stop signaling their interest in alternatives with little probability of victory (if it does not win, you do not pay votes), and it solves the problem of minority disenfranchisement: the more elections a subject loses, the more power future electoral power she accumulated. The article uses exact computational methods (GAMBIT is used for backward induction). The simulations indicate that the PAYW part improves a fixed number of votes version of the Storable Votes
SV-PAYW shall be considered as a natural alternative to Quadratic Voting for its use in distributed governance systems (vg. to implement the democratic reforms proposed in “Radical Markets”). In my view is equally simple, and the avoidance of strategic behavior is likely to be more complete. Additionally, the sock puppet problem does not exist in SV-PAYW, because the system is linear and “dividing” votes to more electors does not affect electoral power.
The ideal political workflow
In addition to this technical article, I have written this other, much shorter one, about the integration of “preferences” and “knowledge” in governance systems. In my view this paper formalizes the main intuition in Robin Hanson Futarchy system:
This philosophical article was the inspiration to work in voting systems. The main idea was that a political system is not legitimate because of the consent of the governed, but because of the welfare of the governed. A political system for me was a mechanism that collected information about preferences and facts and turned them into decisions. I already commented that idea in non-technical fashion in the EA Forum in the post “No Room for Political Philosophy”.
Holistic visions of democracy expect people to make meaningful opinions on public issues and considers that decision receiving more than half of popular support are legitimate. But the number of decisions is enormous, popular policies are often infeasible and the portfolio of policies that people would take on an issue-by-issue basis would be probably grossly incompatible (sequential voting is not known to have good properties).
On the other hand, if we were able to provide the voter with the set of possible states of nature, they could simply pick the best “state of the world” and at least in formal terms the exercise would be consistent.
My first idea was that voting in the space of possible states of the world would be simply finding some maximum given the utility functions revealed by the participants. But it is obvious that players voting in a large space would try to assess the two points with a maximum probability of being voted by the others, and pick the preferred between those two. This lead me into looking for multi-alternative voting systems, and to the road that lead to SV-PAYW.
I think strategic voting would still be present in this system in the form of strategically abstaining (voting less than your true value) for outcomes that seem likely to win in order to store those votes for future elections. This could lead to a widely popular outcome getting starved of votes. There would also be an incentive to introduce lots of meaningless elections between irrelevant (to you) alternatives in order to abstain and accrue more stored votes.
Could also be described as “There would also be an incentive to allow others to make decisions on issue that matter more to them than to you, in order to be more likely to get your way on an issue you care about.”
Re-phrased that way, it’s not clear to me that this is a bad thing. If they don’t care about those other issues either, then you won’t gain any stored votes on net relative to other voters.
Yeah, it could definitely be more of a feature than a bug.
But it also creates an incentive to bring lots of annoying stuff to vote to force your political enemies to vote for it. For example, if you put “Deport all Rationalists” up for vote as often as possible, you can prevent Rationalists from voting for anything else.
Well, if rationalists are a minority, with no external limits on the agenda, they can be deported anyway.
I only have considered a case with external agenda setting (issues with variable relevance exogenously arrive), as is typical to turn voting into a mathematical problem.
The second paper is about the context of voting systems. What I argue there is that the structure of the voting space is more important than the voting system.
What shall people vote? They shall vote among feasible states of the world.
If voting to do X doesn’t matter because X could be done anyway without a vote, why wouldn’t that apply to other things than just deporting rationalists? The logical endpoint of this is that votes will be useless, because anything that is voted for could be done anyway without a vote.
And if some things can’t be done without a vote, exactly what are they, and why can’t “something that would really harm rationalists” be one of them?
What I claim, is that with enough agenda setting manipulation you can nullify the properties of any voting system.
In my opinion, SV-PAYW is the best “voting system” available, but the mechanism has been analyzed under explicit hypoteses on the randomness of issues to be voted. The stream of political issues (represented by the valuation of the participants of an electoral victory) is supposed to be stochastic i.i.d.
If “deporting rationalists” is possible, and rationalists are not more than half of people, I don’t see what security can they receive under any electoral system. If you can vote “disefranchise group X”, then any minority group can be removed from the political system.
I was about to say that I explicitely deal with that issue on “the ideal political workflow”, but there is nothing to deal with.
If deporting rationalists is possible and rationalists are more than half of people, there’s still no security they can receive, by your reasoning. After all, you’re postulating that it would be possible to deport rationalists before taking a vote on whether to do so. Before the vote, the fact that they’re more than half doesn’t matter.
Like the parent said “Deport all Rationalists” or even “Deport everyone named Arturo Macias” are entirely feasible to accomplish with available resources…
It seems like the more important issue is who gets to decide what to vote on and what is presented for voting?
e.g. if the limit is say 1 vote per day, allowing for sufficient time for reflection and study of the issue at hand assuming perfect allocation of time, there’s still way more then 365 possible things a year to vote on.
This is the whole point of the mechanism. To allocate victories to those who value them more. In the model there is a stochastic flow of issues with stochastic importance for both players.
The idea is that this system allocates victories to those who value them more.
People spend more votes on what they value more. In the original Casella system, every vote you cast, you lose it; my contribution was that you are only charged the votes casted in the winning alternative.
Absolutely incredible nobody suggested this before.
I still recommend you to read (and comment) the second pre- print.
Thank you to everybody for commenting!!
A lot of voting schemes look like effective ways of consensus decisionmaking among aligned groups, but stop working well once multiple groups with competing interests start using the voting scheme to compete directly.
I think the effectiveness of this scheme, like voting systems in practice, would be severely affected by the degree of pre-commitment transparency (does everyone know who has committed exactly what prior to settlement of the vote? Does everyone know who has how many votes remaining? Does everyone know how many total votes were spent on something that passed?) and the interaction of ‘saved votes’ with turnover of voting officials (due to death, loss of election, etc). For example, could a ‘loser seat’ with a lot of saved votes suddenly become unusually valuable?
With regard to transparency, ballot anonymity is necessary so that outside parties seeking to influence the election cannot receive a receipt from a voter who was purchased or coerced. Public precommitment to positions would likely be even more exploitable than public knowledge of who proposed what and who voted in which direction.
Do you have any thoughts in this direction?
SV PAYW is mainly designed for people to signal both intensity and direction of preferences. My opinion is that it is close to optimal to create conditions for truth telling of preferences.
In the situation considered in the paper there are only two players, so they know how many votes have themselves and the other player and the previous sequence of votes. The “incomplete information” situation means that the true value of wining in a given round is public.
While the voting system is very general, the situation considered is very simple, so recursive Nash equilibrium can be computed and simulated.
As commented in the second paper, unfortunately the big question is how to vote, but to create a meaning vote space… the question “what to vote” is in my view the most important. See “the ideal political workflow”.
A small nitpicky practicality comment: in a real world system you can’t allow infinitely divisible votes. You have to choose a large finite number of divisions per vote (e.g. 1e15). If a user can input infinitely small divisions, then they can crash the vote storage system with irrational numbers (e.g. pi).
I am no longer a gifted analyst, but I seriously doubt this. Differential games are well known, with their marvelous fixed point theorems and all the stuff.
In fact, if votes are not divisible you have to lot them, , as you can see in the (clumsy but tractable) discrete version I have analyzed in the paper.
How durable is the vote storage? I can see this as great if there’s a closed set of voters on a closed set of issues, and voters get to allocate the marginal importance to them of each issue, in order to use all their voting power for the most important. I suspect that for long-running governance-choices, this will feel unfair to young/new voters, and to older ones who’ve used their votes on previous things that they now realize were unimportant.
I will also say that I’m worried by the statement
This treats people as moral patients rather than moral actors. That’s a framing that leads to disenfranchisement pretty easily.
How durable is money? In this version there is a fixed amount of votes circulating among voters, and votes can be stored indefinitely.
Of course, if this model were successful, versions with “storage costs” could be considered. Let 1000 flowers blossom!
That answer just raises more questions. How do new voters get votes, and what happens to deceased or newly-ineligible voter’s “stored votes”? Are votes transferable (or sellable)?
Money is very rather different from votes; there’s zero expectation of “fair distribution” or “equal weight”. That’s why we have different things for different purposes.
You COULD just do away with voting and use currency auctions. I think a lot of people would object.
This is the QV and I find it wrong. With money, at the end pivotal votes are only those of the largest money owners. Who can give money for collective choices? Those that can recover it, because their wealth is so large than individual consequences of collective decision is individually profitable. Keeping the political system separated from general purpose currency is critical (the Casella and Mace review agrees). The system as described in the paper is totally parallel to currency, while it works like it in the sense that you only pay votes when you get your alternative.
In SV PAYW the fixed number of votes is redistributed among voters after any election (votes casted in the winning alternative are those “payed”) in a one-vote one-man way. Even with no new votes for new players (and the votes from the dead are available for redistribution), new voters receive votes from the winners of each election.
A final remark: SV PAYW is more spectacular, but “the ideal political workflow” is more important.