Bill Clinton: “if you don’t vote, it’s half a vote for the other guys” – just heard on CNN at a campaign event.

This is a property of elections that hadn’t occurred to me. The quantity Clinton cares about is C – T, where C is the number of votes for Clinton and T the number of votes for Trump.If this is positive, Clinton wins; if it’s negative, Trump wins. If you vote for Clinton, that goes up by 1; if for nobody, it doesn’t change; if for Trump, down by 1. So not voting is makes this margin one less than Clinton would like; voting for Trump makes this margin two less. Hence, half a vote for the other guys.

(My vote can be inferred from my choice of sign convention in this post.)

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Clinton presumably cares more about sign(C*-T*) where C* and T* are electoral college votes. C_tx-T_tx or C_ma-T_ma probably means a lot less to either candidate than C_oh-T_oh. Exactly what the relative values are is a fun game. Come to think of it if you think a third party might grab a electoral college vote then I’d guess she’d case more about sign(C*-269).

This argument in the context of South African politics (and presumably other places as well) has always struck me as interesting. I’ve heard “A no-vote is a vote for the ANC”. As we have proportional representation and no clumping by state/province if I think the ANC gets 62% (sans my vote) then it feels like a no-vote is 0.62 votes for the ANC (equivalently 0.3 votes for the DA and 0.08 for the EFF)? On the other hand if I think of the odds of my vote changing the number of seats that one party gets then all the major ones seem equally likely to have the marginal seat changed, which makes it feel like 0.333 votes for the ANC. Voting for a small party on the brink of getting a seat (or a second seat) then seems to have a higher impact but how many votes that counts as I have no idea.

The “half-vote” reasoning is the same as used in Baseball to calculate how many “games behind” a team is. Playing a game against the leader will change the games behind by 1 (either forward or backward), but playing a game against someone else will only change the games behind by 1/2.