• This incentivises some weird stuff.

In this setup, individuals are represented by vectors of length in dimensional space. (where is the number of issues voted on) The combined vote is just the sum of all the vectors. Collusion just means adding the vectors, and then pointing both vectors in that direction.

Red and blue are the 2 voters (red is richer). Purple is the combined consequence of the votes. Dotted red and blue are what happens when they collude.

Lets suppose its a token based vote, and everyone has 1 token.

Everyone else is a naive pro puppy (up) voter. You are a strategic pro frog voter.

If you vote your actual preferences, the result is as shown above. Your preferences to pro frog get combined with the puppy lovers. However, you could vote almost entirely anti puppy, with only a trace of pro frog. The pro and anti puppy sections almost cancel out, meaning that when your vote is colluded with that of a puppy lover, you get 2 (almost) entirely pro frog votes.

(There is another sensible means of colluding, that’s having the same results on the election, but spending less money to do it. So this would give people partial refunds, and not change the result. This kind of encourages voting for really unpopular positions, but doesn’t directly change the election result. Its basically the top diagram, except the dotted arrows are scaled down so that they add to the purple arrow.)

• I’ve been noodling on an example, and did notice this kind of problem. Currently working on what would happen if collusion was limited to vote trades between pairs of issues you directionally agree on. So only “I vote +1 puppy, +2 frog; you vote +2 puppy, +1 frog; we transform into +1.58 puppy, +1.58 frog apiece”.