Wednesday, January 23, 2008

Optimizing your vote

First off, I am delighted that Lance is back! I don't think this picture of Lance looks like him. I'm looking forward to meeting Jason and Nicole (at CCC 2008?) to see if they look like themselves. Second off- A post on politics.

This is not a post expressing any particular political viewpoint. Here is the question: Is it always best to vote for who you actually like best in the primary elections?

Consider the following scenario. I use real names, but the ratings are made up just for this problem and do not reflect mine or Lance's opinions.

Say you rank the current candidates in the following order with the following scores on a 10 point scale:
  1. Obama: 8.8 (acceptable) Democrat
  2. McCain: 7.8 (acceptable) Republican
  3. Paul: 7.5 (acceptable) Republican
  4. Clinton: 7.0 (acceptable) Democrat
  5. Edwards: 6.8 (acceptable) Democrat
  6. Thompson: 6.0 (not acceptable) Republican
  7. Huckabee: 5.8 (not acceptable) Republican
  8. Romney: 5.0 (not acceptable) Republican
Also say that you are in a state where you can vote in either the Democratic or Republican primary (but not both). We could also have numbers for how likely they are to win the nomination (e.g., why vote for Ron Paul when he doesn't have a chance). We could also have numbers for each pair of Republican and Democrate as to who would win the general election (e.g., you may vote for Huckabee because you think that Obama, Clinton, and Edwards all have a good change to beat him in the general election, so you want him to be the nominee. Of course, this is a dangerous strategy since he might win and you didn't think he was acceptable. Also, you DID like McCain so...)

Given all of this data, who should you vote for? Can this problem be made rigorous and solved? Of course, the really hard part in the real world might be getting those numbers. And you may have other reasons to vote, as shown by this ad:


  1. Have you seen this site, devoted to the topic of Declared Strategy Voting?

    I did a bit of analysis on the method as part of an undergraduate project, and found that sometimes the outcome of an election was unstable and depended upon which votes were counted first.

    If I remember correctly, it is impossible to create a fair voting system (where fair has some mathematical criteria) with more than two participants.

  2. It seems common knowledge that game theory thus far has not been able to predict why millions actually do vote. I think we need a different model.

    David Parkes did some mechanism design work that takes into account the effort expended to collect data in order to bid more appropriately. Using any such model in this case, the cost of collecting the data far outweighs the expected return from voting wisely. This certainly takes more into account, but here is still not the right model.

    Any suggestions?

  3. > .. it is impossible to create a
    > fair voting system (where fair has
    > some mathematical criteria) with
    > more than two participants.

    If by "participants" you mean "candidates", then this is true, and is called Arrow's Theorem. But that doesn't mean you can't find a better (fairer, more robust, higher expected utility) then the current one!

    Warren Smith has done some rather exhaustive simulations and makes a convincing case that Range Voting is the best currently known voting system for a choose-1-of-n election. See

  4. Regardless of your preferences, you shouldn't vote at all.

    That said, of course I will vote, because it is a moral requirement, even if it might be individually illogical. But I won't bother with this kind of strategizing, because that is doubly illogical.