Advance warning: I’m pretty sure this is a bad idea. I’m sharing it because I think it might be an interestingly bad idea. Or maybe it makes a better game mechanic than democratic system, I don’t know.

The starting question from this was: How would you design a voting system for a parliamentary government (that is, the system that the parliament itself uses, not how they are elected) so that it encourages compromise and finding acceptable middle grounds rather than just doing straight up majority rule?

The key idea is to make in an explicit system of trading influence (to replace or augment existing implicit systems of trading influence). On questions you are mostly indifferent to, you can trade your vote away for influence on later votes.

In order to do this, we introduce a system of virtual currency representing influence. The currency is given value through an annual tithe, designed such that the amount of influence in circulation is only sufficient for, say, 80% of parliament to pay the tithe. Anyone who cannot pay the annual tithe drops out and comes up for re-election (thus creating a system of rolling elections). Some sort of additional term limit is probably required too.

Votes for or against a bill are then cast as follows:

Each representative casts one of two types of votes:

• a firm vote, which is a vote for or against plus an amount of influence the representative is willing to spend to ensure that vote.
• a tentative vote, which is an abstention plus an amount of influence the representative would require to cast their vote for or against.

Once the vote is cast, the auction begins. I’m a little unsure on the optimal design of the auction here. I believe the following is reasonable, but I’m pretty sure it’s not optimal (for any sense of optimality). The design is basically that of a Vickrey Auction, but with votes instead of influence.

For each side, we determine the number of purchasable votes: That is, counting from the smallest offer upwards we buy votes until we would require more influence than we have allocated left to spend. However many we bought is our set of reachable votes.

For each side we add up the number of purchasable votes with the number of firm votes cast for that side. This gives the number of accessible votes.

If both sides have the same number of accessible votes, that’s a tie. Move to tie breaking procedure (e.g. default against the bill) and nobody pays anything.

Otherwise, whichever side has the larger number of accessible votes wins the vote but must purchase votes to the tune of one more than the other side’s accessible votes (this may be zero votes) using their influence. This works by buying up votes starting from the cheapest until you’ve purchased enough votes. The cost of these votes is then distributed amongst the people paying for them using a system I described previously that basically splits the bill evenly amongst everyone who can afford it, and everyone who can’t afford the even split pays their whole budget.

I don’t think this encourages entirely honest play unfortunately – although the vickrey mechanism forces you to be honest about the number of votes you need, it’s a bit too disconnected from the actual bids (and I don’t think people are encouraged to be honest in the prices they set their vote at at all?) but it’s probably not too bad. Insert better auction design here.

Problems

There are a number of obvious problems with this and probably some more non-obvious problems with this.

The fundamental problem with using any sort of currency mechanism for voting is what you do when someone submits the same bill twice. I think this is fixable here by having a “parliamentary behaviour” notion that when you’re bought you stay bought. In order to enforce this it may be useful for MPs to declare blacklists where they refuse to buy votes from certain candidates.  This complicates the calculation of how many votes are accessible significantly (I think it may turn it NP-hard. It’s certainly solvable through a mixed-integer linear program, but that starts to sound like something you don’t want in your voting procedure).

This is vulnerable to bad actors who just always put their vote up for sale, taking currency out of circulation and thus increasing turnover in the parliament. By doing this preferentially only when the makeup of the parliament is not to your liking it might be possible to stack the parliament that way.

If you have either term limits or are obviously not going to be re-elected because it’s coming up to tithe time and you don’t have even close to enough influence it creates an incentive to just go wild on your spending. Of course term limits already do that.

It’s unclear how this interacts with party systems and party whips. I’d like to avoid that by having more fluid parties and no party whips, but I think reality may work against me on that one…

Advantages

Well I think it’s interesting, and interesting is obviously good, right?

But the concrete advantage of it is that by creating a system of trading influence fairly explicitly it creates a much firmer platform for small parties who are really mostly interested in a core set of issues to get influence over those issues while achieving a sort of “compromise liquidity” for the larger more influential parties.

Moreover, in systems with small parties you already have this sort of influence trading happening, only it’s behind the scenes and thus illegible to the public. By making it official and part of the system you get greater public oversight into what is going on.

Over all, I think the disadvantages beat the advantages by some margin, but maybe that will give the undecided middle some interesting influence that they can spend on a better system later…