The endorsement game

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Consider the following two-dimensional voting problem: In a two-party system, call the parties A and B, the electorate -divided into a majority and a minority- chooses their preferred candidate along two dimensions. First, voters are more likely to vote for a candidate representing their population subgroup and secondly, they care about the candidates’ political views.

Assume voters to be uniformly distributed over the unit interval in terms of their ideology. The current incumbent from the majority subgroup of the population belongs to party A and supports a median policy. Party B does not have a suitable candidate from the majority subgroup of the population but two promising minority candidates. It is immediate to see that in the simple voting model the minority candidate has no chance of winning the election. What about party B positions its candidates in the primaries to the left and right of the incumbent and has the looser endorse the winner? Assume an endorsement not to guarantee votes but to increase the likelihood of voters initially opting for the endorsing candidate to vote for the endorsed one. Now the primary winner could move for moderation in the main election and reap the benefits of endorsement.

Do we have models which shed light on this scenario?

Is there a Monty Hall problem in Who wants to be a Millionaire?

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The basic Monty Hall problem has been discussed far too often to keep track. In his blog, my former teacher Ulrich Berger briefly discusses a conversation appeared on “Who wants to be a Millionaire”:

A candidate faces a multiple choice question with four possible answers, only one of which is correct. She doesn’t know the answer and attaches a probability of 1/4 to each alternative. She chooses A however, not based on any knowledge. Then, before confirming her answer, she recalls that she hasn’t made use of her 50:50 joker, a random mechanism deleting two out of the 3 wrong alternatives. If the candidate chose A for herself before applying the joker and A remains one of the two alternatives on her screen, should she stick to her choice or switch to the other alternative?

Applying to multiple specialties in the medical resident match

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The main resident match by the clearinghouse NRMP (National Resident Matching Program) is for several reasons far more complicated than portrayed in the media or stylized in academic models. Simplification in many cases is perfectly acceptable and an art by itself. However, one of those complications is the fact that within the program actually various “sub-algorithms” are run due to the vast number of different clinical specialties, exceeding 40 in 2015. What is more, about half of the students tend to apply for more than one specialty, in general two with a very small number ranking residency programs of more than three specialties. Some sources on the internet designed to help students through the match argue that data seems to suggest that students increase their chances of a match the lower the number of specialties they apply for. In fact, in of all applicants to Neurology -a specialty with rather few openings- for instance the 2013 NRMP matched 63% of students applying for a single specialty, 59% of students with 2, 48% with 3 and 29% with four or more. Outcomes appear to be similar for other specialties independent of the number of vacancies. Based on this evidence it is suggested that students optimize by choosing a single specialty. This is outrageous inference since this claim’s validity depends on various circumstances. Without detailed knowledge of the data I am fairly certain that this statistic is merely caused by an endogenous selection problem. Students with a strong background in possession of excellent reference letters by professors relevant in their field will expect to be matched in their preferred specialty and forbear from applying to different specialties to spare themselves and their advisors the need to explain their dedication to one field over the other. Weaker students though, more uncertain whether they make it or not, will diversify their applications as an insurance policy. It would be interesting if someone were to look closely at the data and attempts to analyze whether fewer specialties are beneficial among weaker candidates. In fact, the opposite might hold true. On the other hand, given limited information about students’ qualities, the number of specialties might actually serve as a signal of quality and confidence and the claim might be correct. This, however, would be obsolete if all students were to apply for a single specialty. Concluding, there is certainly no clear answer to this question without a profound analysis.