# 13

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The US Congress is trying to resolve the national debt by getting hundreds of people to agree on a solution.  This is silly.  They should agree on the rules of a game to play that will result in a solution, and then play the game.

Here is an example game.  Suppose there are N representatives, all with an equal vote.  They need to reduce the budget by \$D.

1. Order the representatives numerically, in some manner that interleaves Republicans and Democrats.
2. "1 full turn" will mean that representatives make one move in order 1..N, and then one move in order N..1.
3. Take at least two full turns to make a list of budget choices.  On each move, a representative will write down one budget item - an expense that may be cut, or something that may become a revenue source.  They may write down something that is a subset or superset of an existing item - for instance, one person might write, "Air Force budget", and another might write, "Reduce maintenance inspections of hanger J11 at Wright air force base from weekly to monthly".  They can get as specific as they want to.
4. If there are not \$2D of options on the table, repeat.
5. Each representative is given 10 "cut" votes, worth D/(5N) each; and 5 "defend" votes, also worth D/(5N) each.  A "defend" vote cancels out a "cut" vote.
6. Each representative secretly assigns their "cut" and "defend" votes to the choices on the table.
7. Results are revealed and tallied up, and a budget will be drawn up accordingly.

What game-theoretic problems does this game have?  Can you think of a better game?  Is it politically better to call it a "decision process" than a game?

The main trouble area, to my mind, is order of play.  First I said that budget items would be listed by taking turns.  The 1..N, N..1 order is supposed to make neither first nor last position preferable.  But taking turns introduces complications, of not wanting to reveal your intentions early.

Then I said votes are placed secretly and revealed all at once.  This solves problems about game-theoretically trying to conceal information or bluff your opponent.  It introduces other problems, such as tragedy-of-the-commons scenarios, where every Republican spends their "defend" votes on some pork in their state instead of on preventing tax cuts, because they assume some other Republican will do that.

Is it better to play "cut" votes first, reveal them, and then play "defend" votes?

Is there a meta-game to use to build such games?

# 13

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The US Congress is trying to resolve the national debt

That's just not true.

Results are revealed and tallied up, and a budget will be drawn up accordingly.

I'm having trouble figuring out what algorithm you have in mind for drawing up the budget from the voting results. Please be more specific? For example, what happens if everyone votes to "cut" the same items, as a result of which the "cut" items do not add up to \$D?

Is there a meta-game to use to build such games?

How to build such games is studied under the name mechanism design, so I guess one could consider that whole academic field to be such a meta-game.

I'm having trouble figuring out what algorithm you have in mind for drawing up the budget from the voting results. Please be more specific? For example, what happens if everyone votes to "cut" the same items, as a result of which the "cut" items do not add up to \$D?

ISTM the most sensible way would be to sort items by "cut" score and add them up until you arrive at \$D total, using the time the items were nominated as a tie breaker.

The votes are denominated in dollars. Each budget item has an amount cut from it (or added to it, if it's a tax) equal to the sum of the values of the votes.

Upvoted for being:

• an interesting idea that I hadn't thought of

• a non-mindkilling post about politics (in particular, it's not clear from the post whether the author supports either faction)

• upfront about potential problems with the idea

• suggestive of ways to make further progress

How to solve the national debt deadlock

In GetDefaultCountry()?

This is a good example of the classical way that intellectuals and nerds (like most of us at LW) fail. We can construct really interesting theoretical constructs that have zero hope of being implemented.

What's wrong with coming up with an interesting theoretical construct that has almost zero hope of being implemented? Can't that be a vehicle for improving understanding? I don't see any failing in that. It's not like PhilGoetz was recommending we all start lobbying congress and spreading the word in the media about his idea.

Like that "democracy" thing. Silly intellectuals.

Coming up with a solution is not a fail.

Like that "democracy" thing. ... Coming up with a solution is not a fail.

Great work lab boys! Now all we need is a problem.

We can construct really interesting theoretical constructs that have zero hope of being implemented.

I thought you were going to finish the sentence as "...zero hope of working." As it is, you don't seem to be making a valid criticism. Suppose a group of people faced a similar situation. They could implement this solution and succeed.

I fail to see how this wouldn't collapse to precommitting and group action immediately. The majority side could always get what it wanted at little to no cost to itself. Republicans for example could put "All of Obamacare, unemployement, Social Security, and any other socialist programs" five times in slight variations, and allocate all their cut votes to it. There are 240 republicans and 195 democrats, which would result (if I understand your system) in a 10% cut to those programs. Or more if you're allowed to count it 5x times. Subsequent iterations of the game would cut it by more and more each year. They would be free to block the other side with their defend votes as usual.

The granularity of nominations would be an issue. You could kill programs with sufficiently precise cuts. For example if you wanted to end foreign wars you could separate out "All gasoline used in the military abroad", "All the food used to feed soldiers abroad", "All the bullets and munitions used abroad", or "All the electricity used by our military abroad". Each one is incredibly cheap (relative to the cost of the entire war) but successfully cutting any one to zero would end the war and achieve your goals. The same method could be used to kill many other programs.

Also, it would be necessary to do cuts before defends. Otherwise, you could have a situation where there are 27 variants of "Cut all of Unemployment Benefits" (with some slight caveat to make them unique), and all members of one side vote to cut the same one while the members of the other side are spread out trying to defend them all.

As it happens, there are more Democrats than Republicans in the Senate. Since in the end both houses must agree on a budget, perhaps the actual thing to do is to give each party the same number of votes, divided in some way between their senators and representatives.

As for whether in fact every year the budget would change in one direction, that assumes that cuts will continue to need to be made. It's not clear how you determine the level of cuts (or increases) to be made under this game. Also, the notion that the party in power has more influence on the budget seems to me to be a benefit from the perspective of democracy, rather than a negative.

I agree that granularity is a potential problem.

The basic problem is that, once the budget is drawn up, it still has to be approved by a majority vote...

If they wanted to, they would be able to usefully precommit by way of changing that law.

If they don't want to, they wouldn't want to play this game in the first place.

True enough.

I'm not sure how familiar with voting theory (or cake cutting theory) the average LessWrong reader is, so I may be preaching to the choir. But Arrow's theorem (You can wiki it, I can't give a precise mathematical definition off the top of my head.) pretty much states that having a decent voting system is impossible. Of course, we use the worst one possible (plurality) so anything would be an improvement. But mathematically, any solution proposed here will not be perfect, or perhaps even any good.

Arrow's Theorem is a lie. Not really, but it is widely misinterpreted.

That's interesting. Thanks for linking to that. As I said in my other comment though, there are still significant problems with that voting system - even if it does technically meet all of Arrow's criterion. It encourages strategic voting to a tremendous degree, as you have no incentive to give any points to a candidate that you don't want to see win. In that sense, it would likely result in an election almost identical to approval voting - which doesn't fit Arrow's criteria.

If you could trust voters to actually rank their preferences, then almost any voting system would work well - it's just a question of opinion on which you think is "fairest". I'm a IRV person, myself. Or a slight modification thereof. But I digress.

When it comes to large scale voting systems, I actually think that because of the Public Good nature of intelligent voting, voters are likely to vote with prosocial intent but also irrationally (they want the government to be good for people in general, but they favor stupid methods for doing that; see this). Thus the major problem large scale voting systems have is not the design of the voting system but with poor decision making on the part of voters. I actually have a proposal for taking advantage of prosocial voting but encouraging more intelligent voting decisions (link). I do not claim it is likely to ever get enacted.

The article you cite is incorrect. The proposed ranged voting counterexample does not satisfy Independence of irrelevant alternatives.

I don't have an opinion on whether the particular mechanism McCabe gives is a good one or not.

However, the point that Arrow's theorem does not prove what many people say it proves is solid. Arrow's theorem does strongly suggest that multi-agent decision mechanism design is difficult, but it does not prove that 'good' decision mechanisms are impossible.

However, the point that Arrow's theorem does not prove what many people say it proves is solid.

No it is not. The argument was that Arrow's theorem applies to voting systems in which voters state their preference rankings for the options, but what about voting systems in which voters give different information? This is a map-territory error. Whether or not the voting system is directly told about the voters' preference rankings, it cannot in all cases yield a decision satisfying the desired criteria. Arrow's theorem holds.

I did not intend to disagree with this. The lessons I have drawn from that post (and other related material) is that lots of people over interpret Arrow's theorem thinking it proves something like RobertLumley statement "pretty much states that having a decent voting system is impossible." even though there are things which you might want to call 'voting systems' which (but violate the conditions of Arrow's theorem) and have nice properties. In other words, lots of people think Arrow's theorem proves you can't have good collective decision making algorithms, but it only applies to a certain subset of algorithms, so other kinds of algorithms may be 'good'. I do agree that Arrow's theorem suggests "designing a good collective decision system is hard".

In case it's still relevant, I don't see how that is a map-territory error.

That comment is a misinterpretation of the mathematical definition of IIA - but it does raise a good point. The proposed system would, in actuality, be rather poor, it would encourage strategic voting to a tremendous degree, which would make it almost exactly like approval voting - which doesn't fit all criteria.

Odd that you should mention cake-cutting theory, because it says the opposite of Arrow's theorem.

My recollection from the class was that cake cutting was impossible to be done fairly as well, but we only briefly discussed it for about 30 minutes. In reading Wikipedia, it seems I'm wrong - it just takes many, many cuts. Thanks for correcting me.

If I had taught that class I would have emphasized that Arrow's theorem involves discrete choices. There are many ways around it using continuous choices. Thus, cake cutting should not be surprised.

Also, I would have emphasized n=2. Arrow's theorem is obvious in that case. And everyone knows how to cut cake into two pieces.

Yeah, it seems as though that would have been a better approach. I never got that.

But the class was almost three years ago and it was just a one credit hour Credit/No Credit "freshman honors symposium". It wasn't exactly the most rigorous of introductions.

But Arrow's theorem (You can wiki it, I can't give a precise mathematical definition off the top of my head.) pretty much states that having a decent voting system is impossible.

In that case, we should reinstate the monarchy right now, since no system of voting is worthwhile.