You are a member of the House of Representatives, which contains equally sized b

Question

You are a member of the House of Representatives, which contains equally sized blocs of liberals, moderates, and conservatives. The House is considering a conservative bill (B). You are a liberal member and would prefer that the bill not pass (N). A colleague has come to you with an idea: attach a rider amendment (R) to the bill that the conservatives will strongly dislike (but that appeals to moderates and liberals), in hopes of killing the bill. You assess that each bloc’s preferences over the original bill, the bill plus rider, or the status quo are as follows:

Liberal: N > R > B

Moderate: R > B > N

Conservative: B > N > R

If you offer the rider, it will be compared in a head-to-head contest against the original bill (R vs. B), and then the winner of that vote will face the ‘do nothing’ option (winner vs. N). If you do not offer the rider, then there is simply a single vote between the bill and nothing (B vs. N).

2.3 Assume that all legislators will vote sincerely in any pairwise comparison. Should you offer the rider? What will be the ultimate outcome if you do?

2.4 Assume that legislators may vote strategically if it is in their best interest. Can you prevent passage of the bill (B)? Why or why not?

Explanation / Answer

Answer to 2.3)

If the rider is provided then the contest would be between R vs B

In this case looking at the preferences: for moderates & liberals rider is the first and second priority respectively

Likewise, for conservatives & moderators bill is the first and second priority respectively

And since each of the two categories is of equal size, we get 50% chance of the rider and the bill to win individually

.

Answer to part 2.4)

Since the house is considering a conservtaive bill , and if the decision is taken in best interest, it would not eb possible to pprevent the passage of the bill. Because logic and ultimate benefit through the bill serves the main motivation for passing the bill

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