Richard Ngo's Shortform

Richard_Ngo

Random question I’ve been thinking about: how would you set up a market for votes? Suppose specifically that you have a proportional chances election (i.e. the outcome gets chosen with probability proportional to the number of votes cast for it—assume each vote is a distribution over candidates). So everyone has an incentive to get everyone who’s not already voting for their favorite option to change their vote; and you can have positive-sum trades where I sell you a promise to switch X% of my votes to a compromise candidate in exchange for you switching Y% of your votes to a compromise candidate.

What makes this complicated is that I don’t just care that I get votes for my favorite candidate, I also care about where those votes come from - i.e. would they otherwise have been cast for my second-favorite candidate, or for my least-favorite?

EDIT: oh, I think this is equivalent to impact certificates actually.

Some attempts:

Each person starts off with a vote and can sell shares in it to whoever they like for whatever price they like. When the vote is called, you get a number of votes proportional to your shares. This might help me trade votes in a current election for votes in a future election, but it doesn’t seem to really address the core problem that the votes need to be from a specific candidate, that’s what you’re buying, otherwise there’s no benefit to trade in the one-off case.
EDITED: Let a certificate x:A->B be a promise to switch x fraction of your vote from A to B. (I’ll mostly skip the x for brevity.) Suppose your actual favorite candidate is C; you can generate up to one certificate C->Z, for any Z. Then when the vote is called, everyone votes for their favorite candidate, then the votes are modified by all the certificates in circulation.
1. Ideally the thing you’d want is to incentivize the following: “oh, nobody has realized yet that D is a really good compromise candidate between X and Y! I can profit off this fact…” This can be modelled as there not yet being much demand for X->D or Y->D, so you can buy a bunch of it cheaply and wait for the price to appreciate (because many others will also want to buy it once they realize); or maybe you can short X->Y and Y->X; or sell versions of X->Y which are actually X->D->Y. You probably also need the ability to borrow from the bank for liquidity - and maybe the bank should accept A->B->C as a return on A->C?
2. This setup strongly incentivizes strategic declaration of who your favorite candidate is. But maybe that’s just unavoidable… the whole point of a market is that you’ve got something to trade, and in some sense that has to be your default vote.
3. How do markets in general avoid this? By setting regulations saying you can’t make someone’s life worse then tell them to pay to stop. Without political intervention in general markets are just threat-machines. I.e. you really need the distinguished “zero” point in order to make them work.
I think the thing I’m looking for might be analogous to the shift from the COCO equilibrium to the ROSE equilibrium.
1. The CoCo value could be viewed as starting at a disagreement point, and going “let’s move to the Pareto frontier and evenly split the gain”. Which seems like what’s happening with trades in this market, you benefit from how bad your disagreement point is.
2. Diffractor describes a ROSE point as anywhere where, if you drew two lines at the highest utilities that players 1 and 2 could get without sending the other below the disagreement point utility, there’s a tangent line at the ROSE point that has equal distance to the two max-utility boundaries.
3. I don’t really see how to generalize this to constructing a market, nor do I know if that question makes sense.

Richard_Ngo3y*70

4Measure3y

Just spitballing here: Assign each voter 100 shares for each candidate. To vote, each voter selects a subset of their shares to constitute their vote. Voters can freely trade shares. Under this system, a voter would more highly value shares for candidates that are either very high or very low in their preference order (the later so as to exclude them from the vote). Thus, trades would look like each party exchanging shares about which they are themselves ambivalent to gain shares that are more valuable to them. If you remove the proportional chances part, then it becomes a guessing game of which marginal votes actually matter.

Richard_Ngo3y20

Interesting! Hadn't thought of this approach. Let's see... Intuitively I think it gets pretty strategically weird because a) who you vote for depends pretty sensitively on other peoples' votes (e.g. in proportional chances voting you want to vote for everyone who's above the expected value of everyone else's votes; in approval voting you want to vote for everyone you approve of unless it bumps them above someone you like more), and b) you want to buy from your enemies much more than from your friends, because your friends will already not be voting for bad candidates. But maybe the latter is fine because if you buy from your friends they'll end up with more money which they can then spend on other things? I'll keep thinking.

Richard Ngo's Shortform

6

Ω 3

Richard Ngo's Shortform

6

Ω 3