I was thinking last night of how vote trading would work in a completely rational parliamentary system. To simplify things a bit, lets assume that each issue is binary, each delegate holds a position on every issue, and that position can be normalized to a 0.0 − 1.0 ranking. (e.g. If I have a 60% belief that I will gain 10 utility from this issue being approved, it may have a normalized score of .6, if it is a 100% belief that I will gain 10 utility it may be a .7, while a 40% chance of −1000 utility may be a .1) The mapping function doesn’t really matter too much, as long as it can map to the 0-1 scale for simplification.
The first point that seems relatively obvious to me is that all rational agents will intentionally mis-state their utility functions as extremes for bargaining purposes. In a trade, you should be able to get a much better exchange by offering to update from 0 to 1 than you would for updating from 0.45 to 1, and as such, I would expect all utility function outputs to be reported to others as either 1 or 0, which simplifies things even further, though internally, each delegate would keep their true utlity function values. (As a sanity check, compare this to the current parliamentary models in the real world, where most politicians represent their ideals publicly as either strongly for or strongly against)
The second interesting point I noticed is that with the voting system as proposed, where every additional vote grants additional probability of the measure being enacted, every vote counts. This means it is always a good trade for me to exchange votes when my expected value of the issue you are changing position on is higher than my expected value of the position I am changing position on. This leads to a situation, where I am better off changing positions on every issue except the one that brings me the most utility in exchange for votes on the issue that brings me the most utility. Essentially, this means that the only issue that matters to an individual delegate is the issue that potentially brings them the most utility, and the rest of the issues are just fodder for trading.
Given the first point I mentioned, that all values should be externally represented as either 1 or 0, it seems that any vote trade will be a straight 1 for 1 trade. I haven’t exactly worked out the math here, but I’m pretty sure that for an arbitrarily large parliament with an arbitrarily large number of issues (to be used for trading), the result of any given vote will be determined by the proportion of delegates holding that issue as either their highest or lowest utility issue, with the rest of the delegates trading their votes on that issue for votes on another issue they find to be higher utility. (As a second sanity check, this also seems to conform closely to reality with the way lobbyist groups push single issues and politicians trade votes to push their pet issues through the vote.)
This is probably an oversimplified case, but I thought I’d throw it for discussion to see if it sparked any new ideas.
The first point that seems relatively obvious to me is that all rational agents will intentionally mis-state their utility functions as extremes for bargaining purposes.
Because we’re working in an idealised hypothetical, we could decree that they can’t do this (they must all wear their true utility functions on their sleeves). I don’t see a disadvantage to demanding this.
If what you say is true about all trades being 1-for-1, that seems more like a bug than a feature; if an agent doesn’t have any votes valuable enough to sway others, it seems like I’d want them to be able (i.e. properly incentivized) to offer more votes, so that the system overall can reflect the aggregate’s values more sensitively. I don’t have a formal criterion that says why this would be better, but maybe that points towards one.
I was thinking last night of how vote trading would work in a completely rational parliamentary system. To simplify things a bit, lets assume that each issue is binary, each delegate holds a position on every issue, and that position can be normalized to a 0.0 − 1.0 ranking. (e.g. If I have a 60% belief that I will gain 10 utility from this issue being approved, it may have a normalized score of .6, if it is a 100% belief that I will gain 10 utility it may be a .7, while a 40% chance of −1000 utility may be a .1) The mapping function doesn’t really matter too much, as long as it can map to the 0-1 scale for simplification.
The first point that seems relatively obvious to me is that all rational agents will intentionally mis-state their utility functions as extremes for bargaining purposes. In a trade, you should be able to get a much better exchange by offering to update from 0 to 1 than you would for updating from 0.45 to 1, and as such, I would expect all utility function outputs to be reported to others as either 1 or 0, which simplifies things even further, though internally, each delegate would keep their true utlity function values. (As a sanity check, compare this to the current parliamentary models in the real world, where most politicians represent their ideals publicly as either strongly for or strongly against)
The second interesting point I noticed is that with the voting system as proposed, where every additional vote grants additional probability of the measure being enacted, every vote counts. This means it is always a good trade for me to exchange votes when my expected value of the issue you are changing position on is higher than my expected value of the position I am changing position on. This leads to a situation, where I am better off changing positions on every issue except the one that brings me the most utility in exchange for votes on the issue that brings me the most utility. Essentially, this means that the only issue that matters to an individual delegate is the issue that potentially brings them the most utility, and the rest of the issues are just fodder for trading.
Given the first point I mentioned, that all values should be externally represented as either 1 or 0, it seems that any vote trade will be a straight 1 for 1 trade. I haven’t exactly worked out the math here, but I’m pretty sure that for an arbitrarily large parliament with an arbitrarily large number of issues (to be used for trading), the result of any given vote will be determined by the proportion of delegates holding that issue as either their highest or lowest utility issue, with the rest of the delegates trading their votes on that issue for votes on another issue they find to be higher utility. (As a second sanity check, this also seems to conform closely to reality with the way lobbyist groups push single issues and politicians trade votes to push their pet issues through the vote.)
This is probably an oversimplified case, but I thought I’d throw it for discussion to see if it sparked any new ideas.
Because we’re working in an idealised hypothetical, we could decree that they can’t do this (they must all wear their true utility functions on their sleeves). I don’t see a disadvantage to demanding this.
If what you say is true about all trades being 1-for-1, that seems more like a bug than a feature; if an agent doesn’t have any votes valuable enough to sway others, it seems like I’d want them to be able (i.e. properly incentivized) to offer more votes, so that the system overall can reflect the aggregate’s values more sensitively. I don’t have a formal criterion that says why this would be better, but maybe that points towards one.