Electability

As the 2016 campaign (finally) enters the voting phase, pundits start asking (and answering) the question of who is the most electable in the general election. The reason is that it is rational for voters to vote strategically. Ultimately what a voter wants is to help elect the candidate that give them the most utility. Ideally that would be the candidate that most closely resembles their policy positions. But, what if that candidate is unlikely to win the nomination, could it be "better" to vote for similar, but not as ideal candidate, that may have a better likelihood of winning the nomination? What if that candidate could win the nomination, but would have a lower likelihood of winning the general election against the other party's candidate? I can write another column on strategic voting and utility maximizing decision making, but today I will focus on one thing: electability in the general election.

Preview of results:

1) The Democratic candidates are both more electable than than the Republican candidates.
2) Rubio is the most electable Republican. His conditional probability of victory in the general election has been between 40% and 43% most of the cycle, but Trump is not that far behind. He has been between 37% and 43% for most of the cycle.
3) Cruz is in another class, much less electable than Rubio and Trump. His conditional probability of victory in the general election has been between 25% and 30% all cycle. Never reaching above 26% for the last 10 days.

Polls of theoretical head-to-head matchups are so worthless that I will not bother reading or referring to them. They are so abstract to voters that they have almost no meaning. Rubio v. Clinton, Trump v. Sanders, Cruz v. Sanders? Voters do not know enough about the candidates and what would happen over the next 9.5 months to answer this question meaningfully. But, thankfully, prediction markets do tell us a bunch about this.

We have the probability that a candidate wins the nomination and the probability that that same candidate wins the general election. If you divide the likelihood of winning the general election by the likelihood of winning the nomination you get a rough approximation of the conditional probability of winning the general election. Assume a candidate is 60% to win the nomination and 20% to win the general election. Assume that that candidate will only compete for the general election if s/he gets the nomination. Then 20%/60% = 33% is the probability that the candidate wins the general election, if s/he wins the nomination. In 6 of 10 worlds the candidate compete for the general election. In 2 of 10 worlds s/he wins the general election. That means in 2 of 6 worlds where the candidate competes s/he wins or 33%. This is the same as the NFL playoffs. We are currently in the semi-final rounds. The likelihood of each team winning the Super Bowl is nice, but if you divide that by the likelihood of them winning the Championship games this weekend, that is the conditional likelihood of them winning the Super Bowl, if they win this weekend. For instance, the New England Patriots are 31% to win the Super Bowl and 60% to win on Sunday. So, conditional on winning on Sunday, they are just 52% to win the Super Bowl.

Two key caveats are that this assumes one specific relationship between the two rounds of elections, which does not necessarily hold. And, these numbers are not precise; there is an error bound around this. This is why I only report the results of those candidates with a minimum amount of probability. That being said, the results are pretty clear:

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