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Subject: Quadratic Voting as a game mechanic rss

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Andy Meneely
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I've been reading this great article on Quadratic Voting: http://ericposner.com/quadratic-voting/. The publication they link to is also quite a good read (58 pages, but a well-written 58 pages that even us mere mortals can understand).

Now the paper is all about using quadratic voting as a solution to the "tyranny of the majority" problem. Here's quick description of the approach:

Quote:

Each person can buy votes for or against a proposal by paying into a fund the square of the number of votes that he or she buys. The money is then returned to voters on a per capita basis. Weyl and Lalley prove that the collective decision rapidly approximates efficiency as the number of voters increases. By contrast, no extant voting procedure is efficient. Majority rule based on one-person-one-vote notoriously results in tyranny of the majority–a large number of people who care only a little about an outcome prevail over a minority that cares passionately, resulting in a reduction of aggregate welfare.


Now of course there's all kinds of RSP-ish discussion from this article that, well, belongs in the RSP forum.

But would this work as a game mechanic? Here's a sketch of an idea:

Every player has some sort of engine that is dependent on various resources in a little economy. New bonuses and rules changes come across the table that benefit some players in obvious and non-obvious ways. Everyone votes on whether to approve or reject the bonus. You get a fixed number of "vote bucks" that are used in this quadratic voting process. The source of tension, then, is to properly value the improvement of the bonus in a way that improves your economy over other players.

For instance, the bonus "Every player with a Smithy gets 2 Steel immediately" is up for vote. Larry benefits from this a lot. Curly benefits a little, Mo not at all. Larry spends $16 for 4 Pro votes, Curly spends $4 for 2 Pro votes, so then Mo has to decide if it's worth spending $42 on Con votes to not have this bonus be available. Suppose that he does. Then the $16+$4+$42=$62 pot gets split three ways at roughly $20: Larry and Curly lose the vote, but net $4 and $16 respectively. Mo gets his way but nets -$22.

Math is hard to use in board games, I know, but a lookup table would really alleviate that. The choices would be limited to perfect squares and divisions would be clearly marked (rounding handled somehow)

Would this mechanic work?

Would it be fun?

Are there any games that use a majority-vote mechanic that might benefit from this change?
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Przemyslaw Kozlowski
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andygamer wrote:

For instance, the bonus "Every player with a Smithy gets 2 Steel immediately" is up for vote. Larry benefits from this a lot. Curly benefits a little, Mo not at all. Larry spends $16 for 4 Pro votes, Curly spends $4 for 2 Pro votes, so then Mo has to decide if it's worth spending $42 on Con votes to not have this bonus be available. Suppose that he does. Then the $16+$4+$42=$62 pot gets split three ways at roughly $20: Larry and Curly lose the vote, but net $4 and $16 respectively. Mo gets his way but nets -$22.




Wouldn't Mo have to spend $36 (6^2) to tie the vote or $49 (7^2) to win outright?
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Phil Hendrickson
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Not quite the same thing, but have you looked at the voting mechanism in Lancaster? The effect of the votes is just as you described: players vote on new "laws" that provide rewards to players according to certain criteria. Some laws will clearly reward some players over others. Players have to build up their stock of voting cubes through a few means. When it is time to vote, players get one free vote (yea or nay) and can choose to spend some of their stock of cubes as additional votes in their favor.

It is fun to see when someone wastes many voting cubes on a vote that was not even close to begin with, or doesn't have enough cubes to outvote the rest of the group on a law that clearly favors only the one player.

Voting happens each round on three laws. Of course, other interesting actions also occur each round. The knight displacement mechanism is a fun challenge (but not for easily offended people). If you haven't tried it, Lancaster is certainly worth a play.
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Jeremy Lennert
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I haven't read the paper, but surely there is an assumption that voting is by blind simultaneous ballot? If one player can see how the others have voted before deciding what to do, they obviously have an advantage.


In general, I would not expect good voting systems to make good game mechanics.

Some of the things that make a voting system good are: when you have an incentive to vote your true preference regardless of the circumstances; when the outcome is difficult for any individual or small group to manipulate; and when they treat everyone equally regardless of circumstances.

Some of the things that make game mechanics interesting are: when your optimal move changes depending on the circumstances; when a clever player can manipulate the system to his advantage; and when different mechanics are coupled together so they can interact in interesting ways.
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Jim McCollum
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My brother and I saw this article and are working on a game with this mechanic. Nothing to show yet, but the mechanic intrigued me to.
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Lee Borkman
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Quadratic is a pretty extreme curve. Spend 9 to get just 3 votes? Sounds like a rare event. Now *triangular* gives a more gentle curve, but still provides a substantial penalty for buying more votes.

Compare:
1 4 9 16 25
...with:
1 3 6 10 15

Just pondering out loud...
Thanks,
LBB
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Clay
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Sounds very interesting. I'd recommend having multiple proposals resolve at once though and have the votes placed secretly and simultaneously. This makes the interactions of the votes potentially more interesting and more dramatic but most importantly allows you to condense periods of heavy bookkeeping, number crunching and analysis paralysis into a few big chunks instead of having it be a frequently recurring thing, would likely make the system run more smoothly.

Example:

P1 buys 2 votes for A, 1 against B and 3 for C.
P2 buys 4 against A, 2 against B and 2 against C.
P3 buys 1 for A, 1 for B and 1 for C.

P1 is out $14, P2 is out $24 and P3 is out $3.

A fails to pass, B fails to pass and C passes.

Each player gets $13 back and another meaty slab of presumably eurogame-age ensues for a round or two before the next vote.
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Andy Meneely
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Antistone wrote:
I haven't read the paper, but surely there is an assumption that voting is by blind simultaneous ballot? If one player can see how the others have voted before deciding what to do, they obviously have an advantage.


In real life, I believe it is a "blind" ballot although most people will probably make their votes public.

In a game, I see two approaches: either blind simultaneous, or as an auction.

Antistone wrote:

In general, I would not expect good voting systems to make good game mechanics.

Some of the things that make a voting system good are: when you have an incentive to vote your true preference regardless of the circumstances; when the outcome is difficult for any individual or small group to manipulate; and when they treat everyone equally regardless of circumstances.

Some of the things that make game mechanics interesting are: when your optimal move changes depending on the circumstances; when a clever player can manipulate the system to his advantage; and when different mechanics are coupled together so they can interact in interesting ways.


What I like about quadratic voting is the valuation aspect of it, and if the thing you're voting for truly benefits you then yes, you would have an incentive to vote your true preferences.

As for the other things you point out that make game mechanics interesting - I think all of those can apply to quadratic voting.

Bjork wrote:

Quadratic is a pretty extreme curve. Spend 9 to get just 3 votes? Sounds like a rare event. Now *triangular* gives a more gentle curve, but still provides a substantial penalty for buying more votes.


I was wondering about this too. The paper goes into some interesting math as to why it has to be such a steep curve, although they also state that this voting system works best with lots of voters, which of course is not true of board games.

But maybe that means quadratic voting makes more sense with games of 5-10 players instead of the classic 3-4.

Now with a triangular curve you're also effectively creating more purchasing options. That could be a good thing or a bad thing depending on how central the mechanic is to the game.

The Message wrote:

I'd recommend having multiple proposals resolve at once though and have the votes placed secretly and simultaneously.


I like that idea. It could be overwhelming to figure it all out, like you say, but maybe with the right components it would be fun. It may be more efficient than one-at-a-time.

Maybe just showing the next 5 proposals openly so people know what's coming, but still vote one-at-time.
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Susan F.
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Bjork wrote:
Quadratic is a pretty extreme curve. Spend 9 to get just 3 votes? Sounds like a rare event. Now *triangular* gives a more gentle curve, but still provides a substantial penalty for buying more votes.

Compare:
1 4 9 16 25
...with:
1 3 6 10 15

Just pondering out loud...
Thanks,
LBB


I suspect the extreme curve is necessitated by the "refund" part of the system. A gentle curve (with the expectation that you'll get most of your money back) doesn't incentivize players to be stingy when they don't overly care about the result of a particular vote.
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