@k98kurz My intuition also initially led me to the idea of -2 to +2 scale with 0 as default. I unfortunately do not have my sources in order, but here are the conclusions I came to after further reading:

1. A default mid position has some weird and unexpected consequences. You can get a system which rewards the most unknown candidate.
2. Approval/score/rated systems by their nature create more positive elections with less smear. This was immediately observed in districts which switched from FPTP to Approval. When a voter rates two candidates independently in a 0-5 scale, they have the ability to punish both candidates which participate in dirty politics or reward both candidates who demonstrate bi-partisan cooperation. This is especially true in large fields of say 10-60 candidates.

I am working on writing a literature review of how the behavior or parties are influenced by the electoral system. There is a lot written about how FPTP leads to 2 party dynamics, but I am having trouble finding material related to observed or expected dynamics in STAR and approval.

Links to papers on this topic or related works would be appreciated!

@cfrank Thanks for the feedback! I will keep this in mind. For this trial I will only explore single-winner systems.

My study should be sensitive to:

• Party structure

• Effects of repeated elections (a series of elections can be viewed like a repeated prisoners dilemma. There is are equalibria at lose-lose and win-win. I should be able to discriminate differences in incentives towards either equalibria if they exist.)

• Validate or invalidate certain assumptions about how strategic voters playing well (but not perfectly) might behave

• The types of strategies which are actually nash equalibria in repeated stochastic incomplete information with human players. (strategy which is proven to be optimal in a complete information simultaneous 1-shot game, might not be optimal in a repeated stochastic incomplete information version.)

• Discriminating between strategies which might be optimal in a 1-shot version but bad in a repeated game (stabbing allies for example.)

• Level of exploitation an incumbent or leading coalition can leverage

• Failure modes

My study will not be sensitive to:

• exact values (this method is 5% better than this method).
• declaring a winner between similar methods.
• matching the distributions of real-world elections.
• exhaustive testing

@Toby-Pereira @Lime @Marcus-Ogren
Interested in your opinions on this

If you have an allocation game dividing a budget, a pizza, etc... this game is zero-sum in the sense that a you getting a slice of pizza is a slice that isn't going to me.

If you are negotiating with an agent who you are unsure is altruistic, rational, or spiteful there is a strategic incentive to misrepresent as a spiteful agent. An altruistic agent gets less than their fair share and a spiteful agent gets more than the rational agent if they can credibly convince other agents they are spiteful. It is worth it to pay off a spiteful agent rather than provoke it.

So if you are trying to optimize for the social choice there's a big problem with spiteful agents. With limited information all agents are incentivized to misrepresent as spiteful and over-represent how much they care about minor concerns. And for making social choice with limited resources there is a genuine zero-sum nature to the problem. Rational agents operating in a zero-sum environment will behave spitefully (you having it is negatively correlated with me having it.)

So with that irrationality baked in, if we could magically find what the social choice was, with spiteful agents the social choice isn't very sociable. And spiteful agents should be common under resource constraints. This correlation between individual's utility functions will also heavily restrain the types of group choice sets which exist.

@toby-pereira Thanks for the feedback!

National elections generally take place several years apart and a lot can change in between, and so voters wouldn't be able to apply game theory in the same way as they would with multiple elections close together under the same conditions. And also I imagine people in the study are more likely to be "clued up" than the average member of the public.

One of my goals is looking towards what the long-run equalibria might be after people have figured out the system. So in this way I see that as a plus.

So that raises a question - with multiple elections, will it just be the same conditions each time just to see how the methods behave in these ideal conditions, or will certain variables change to make it more "realistic", or possibly you'd model both? Both would be interesting in their own ways.

In trying to set up the models one of my conclusions is that a "correct" set of parameters doesn't exist. I think instead of trying to make a study "correct" or "accurate" it would be more useful to search for robustness. A common result of repeated games is multiple Nash Equalibria. Another common result is sensitive Nash Equalibria. So if one number changes slightly a whole new set of equalibria might be optimal now. So I think it is important to vary conditions to see if an equilibrium is stable.

Reading on different strategies and failure conditions of voting systems you come across some really weird ones where it is technically optimal to do make some really weird decision. But that often requires very specific information. An important concept I came across while brushing up on my game theory is imperfect and incomplete information. When you change the information available it can sometimes change what the Nash Equilibrium strategy is. There's also an idea that a strategy might not be optimal over any specific set of game parameters but is optimal when you are unsure of the exact parameters. The more limited the information the simpler a game sometimes becomes.

In the traditional formulation of utility and social choice a rational agent is imagined as having a preference matrix over all possible states and the "Social Choice" being the choice which optimizes for a group of agents across all preference matrices to achieve a utopian choice or something.

But a very important a common way that people are irrational is altruism and spite. That is, my utility function is a function of someone else's utility function and ... What's important here for modeling is if you have a group of people, everyone's utility functions/preferred orderings will be systematically correlated by a partial differential equation. Furthermore, altruistic and spiteful behavior is dependent on previous relationships over time, expectations for the future, and system design.

For a 1-shot question this doesn't really change anything and was already priced into many models.

But if you are trying to design a system to fairly distribute a good. Say, government distributing public goods, there are some huge modeling effects to consider. If a government gives out 1 widget there is utility update for:

1. the intrinsic utility of receiving that widget
2. update everyone else's utility function/preference orderings based on altruism or spite.
3. Everyone modifies strategic thinking which changes observed behavior.

Let's consider this example of pay-outs to agents <A, B, C>
<10, 10, 0>
<10, 0, 10>
<0, 10, 10>
<5, 5, 5>
<0, 0, 0>

If the agents are rational then there is a Condorcet cycle.

With altruistic agents (depending on the altruism parameters) there is one Condorcet winner or a cycle from every agent wanting everyone else to have more.

With agents who are strongly mutually spiteful <0, 0, 0> is a Condorcet winner.

So if you internalize spite/altruism into your social choice model, irrationally (or rationally?) spiteful agents might willingly choose nuclear war as the efficient social choice.

I think from a system design perspective it is important to treat utility/preference orderings from the thing being distributed differently from the second order effects of how people feel about each other's feelings. One important finding here is that altruistic/spiteful behavior is a strategy trying to selfishly optimize for a reward. Altruism and spite are learned and evolved behaviors which are evolutionary stable strategies and even learnable by perfectly rational agents. They key is they only make sense in repeated games and in the context of a meta-strategy against other agents.

Spite/altruism can also be artifacts of conscious strategic play. Disproportionate retaliation and 3rd party retaliation of non-compliance are bargaining strategies that exist even without voting. Sending a message can be a utility-maximizing strategy in some contexts.

I guess there are some complex 2nd and 3rd order effects of switching from rational agents to real people.

@Toby-Pereira @Lime @Marcus-Ogren
Interested in your opinions on this

@cfrank Thanks for the feedback! I will keep this in mind. For this trial I will only explore single-winner systems.

My study should be sensitive to:

• Party structure

• Effects of repeated elections (a series of elections can be viewed like a repeated prisoners dilemma. There is are equalibria at lose-lose and win-win. I should be able to discriminate differences in incentives towards either equalibria if they exist.)

• Validate or invalidate certain assumptions about how strategic voters playing well (but not perfectly) might behave

• The types of strategies which are actually nash equalibria in repeated stochastic incomplete information with human players. (strategy which is proven to be optimal in a complete information simultaneous 1-shot game, might not be optimal in a repeated stochastic incomplete information version.)

• Discriminating between strategies which might be optimal in a 1-shot version but bad in a repeated game (stabbing allies for example.)

• Level of exploitation an incumbent or leading coalition can leverage

• Failure modes

My study will not be sensitive to:

• exact values (this method is 5% better than this method).
• declaring a winner between similar methods.
• matching the distributions of real-world elections.
• exhaustive testing

Research Question: A common goal in designing voting systems is to maximize group utility/welfare. But in the real world individuals and sub-groups act selfishly to maximize their own utility. The game theory dynamics of an electorate can be hard to simulate, therefore this research proposal will put participants into a repeated "voting game" to identify nash equilibria empirically.

Methodology- It is empirically observed that groups of voters can be highly correlated. A common modeling simplification for voting theory is considering those blocks as one weighted vote. My method will have human participants make the decisions for the voting blocks instead of attempting to simulate what a selfish imperfect-utility-maximizing person might do. Participants will be screened for competitive people trying to win.

My question to the community is:
What do you want to see tested?
This is a great way to get experimental data points for assessing different voting systems and assumptions. Why hypothesizes would you like to see tested?

Concerns with methodology or validity?
I'm not sharing the full methodology I have planned until I finish the first experiment; but feedback on any concerns or issues with the validity of this type of experiment would be appreciated.

@k98kurz 3-2-1 Voting comes to mind for a method which uses a proper negative vote in the form of a "reject" option which is treated differently

@lime said in ABC voting and BTR-Score are the single best methods by VSE I've ever seen.:

This isn't just hypothetical. The CPE paper shows very strong results for Ranked Pairs under strategic voting. This is well-known to be wildly incorrect: the optimal strategy for any case with 3 major candidates is a mixed/randomized burial strategy that ends up producing the same result as Borda, i.e. the winner is completely random and even minor (universally-despised) candidates have a high probability of winning.

I believe you are referring to this chart? Which shows Ranked pairs and Schulze as doing slightly better than STAR with honest voting. Does Schulze also have some failure mode which makes honest voting not the game theoretical optimal vote?

Warren Smith's concept of Bayesian Regret (adapted into VSE) led to an objective method of analysis for single winner elections which allows researchers to overcome biases and competing metrics of "fairness".

In the 20+ years since that idea no one seems to have adapted Bay Regret/VSE for multiple winners. Proportional systems are typically assessed with a few different methods which boil down to different ways to assess error compared to the popular vote. This is not necessarily the same thing as finding the set of multiple winners which maximizes utility.

I doubt there has been a lack of effort since a fair comparison would let STAR fans assert superiority over even more voting methods. So what is the hold up for assessing utility of PR elections?

@k98kurz My intuition also initially led me to the idea of -2 to +2 scale with 0 as default. I unfortunately do not have my sources in order, but here are the conclusions I came to after further reading:

1. A default mid position has some weird and unexpected consequences. You can get a system which rewards the most unknown candidate.
2. Approval/score/rated systems by their nature create more positive elections with less smear. This was immediately observed in districts which switched from FPTP to Approval. When a voter rates two candidates independently in a 0-5 scale, they have the ability to punish both candidates which participate in dirty politics or reward both candidates who demonstrate bi-partisan cooperation. This is especially true in large fields of say 10-60 candidates.