First post!

Welcome to Arrows Fear Him, my blog for discussing election mathematics. I'm a physicist who at some point became interested in third parties. When this happened, I become interested in alternative election methods, stuff like Approval Voting and Instant Runoff and Borda and Condorect and all that. Turns out, these topics have a lot of math behind them, so I got interested in that. Then I got interested in a very specific problem: Favorite betrayal (see an upcoming post).

We know from the Gibbard-Satterthwaite Theorem that ranked voting methods will always give incentives to vote insincerely (if you don't know what that means, don't worry, I plan to do a post on this for the layman, eventually). However, could you at least make it so that while you might have an incentive to lie, at least you only have an incentive to lie about your second favorite? This way you could still throw your support behind your favorite without penalty.

It turns out that there are such systems. Anti-plurality (the candidate ranked last by the fewest voters is the one who wins) and Approval Voting (you vote yes or no on each candidate, most yeses wins, and saying "yes" to multiple candidates is allowed) are examples. Mike Ossipoff and Warren Smith (see the Center for Range Voting in the links to the right) came up with some more. However, these systems are hard to find. My paper (link at top of page) addresses just how many there are and what sorts of families they fall into. The paper has not been through peer review, but I'm putting it up to get feedback and comments.

So, what do I plan to post on here?

1) My manuscript, of course, as I go through revisions and get feedback. Most of the posts will be on that.
2) For the layman, what are ranked voting methods? What is the Gibbard-Satterthwaite Theorem? What is Favorite Betrayal, and why do you need so much math to study it?
3) Nash equilibria and the Gibbard-Satterthwaite Theorem. I'm not a professional game theorist, but I think I've come up with a neat little insight along these lines, and eventually I'll blog about it.
4) The Electoral College. Not so much the politics of it (it is what it is) but a theoretical and strategic understanding of how it shapes incentives.
5) Any other interesting stuff related to election methods that I feel like blogging.

What won't I be blogging?
1) The IRV vs. other methods food fight. I'll weigh in to a certain extent (in brief, I prefer Approval Voting to Instant Runoff Voting) and explain why, but skirmishing over the efforts to implement IRV is not my thing. I'm glad that there are people pushing for alternative election methods, and I'm not going to get in their way.
2) Politics. My views are what they are, and I admit to having leanings that are a mix of left and libertarian, but I don't want to take that up here.

So, welcome, and stay tuned.