- Elections For The French Presidency Proceed In Two Rounds In 1981 There Were 10 Candi Dates In The First Round The T 1 (941.31 KiB) Viewed 32 times
- Elections For The French Presidency Proceed In Two Rounds In 1981 There Were 10 Candi Dates In The First Round The T 2 (420.08 KiB) Viewed 32 times
Elections for the French presidency proceed in two rounds. In 1981, there were 10 candi- dates in the first round. The top two candidates went on to the second round, which was won by François Mit- terand over Valéry Giscard-d'Estaing. The losers in the first round can then gain political favors by urging their supporters to vote for one of the two finalists. Since voting is pri- vate, we cannot know how the votes were transferred. However, we might hope to infer from the published vote totals how this might have happened, which is your goal in this exercise. Anderson and Loynes (1987) published data on these vote totals in every fourth depart- ment of France: library (faraway) data (fpe) A and B stand for Mitterand's and Giscard's votes in the first round, respectively, while A2 and B2 represent their votes in the second round. C-K are first round votes of the other candidates while EI denotes registered voters. All numbers were measured in thousands. The total number of voters in the second round was greater than the first (we can compute the difference as N). We will treat this group like another first round candidate. Now we can represent the transfer of votes as A2 = BAA + BBB + BCC + BDD + BEE + BFF + BGG + BH + B₁J + BKK + BNN, where i represents the proportion of votes transferred from candidate i to Mitterand in the second round. We can equally well do this for Giscard-d'Estaing, but then the 's will simply be the remaining proportions. We would expect these transfer proportions to vary somewhat between departments, so if we treat the above as a regression equation, there will be some error from department to department. The error must have a variance in proportion to the number of voters, because it will be like a variance of a sum rather than a mean. Since the weights should be inversely proportional to the variance, this suggests that the weights should be set to 1/EI.
Your task Fit the appropriate model and interpret. Observe that the weights do matter (check what happens when we leave them out). Observe that only the relative proportions of the weights matter (try to multiply the weights by 53). Since coefficients ; represent transfer proportions, they are supposed to be between zero and one. Impose an ad-hoc fix by truncating the coefficients that violate this restriction either to zero or one as appropriate? Hint: Refit the model and use the built-in offset function. The offset function means no coefficient will be fit, which is the same as saying the coefficient will be one.