Use the preference table to answer the question.

Question

The preference table shows the results of an election among three candidates, A, B, and C.

  

(a) Using the plurality method, who is the winner?

(b) The voters in the two columns on the right move their last-place candidates from last place to first place. Construct a new preference table for the election. Using the table and the plurality method, who is the winner?

(c) Suppose that candidate C drops out of the new table, but the winner is still chosen by the plurality method. Is the irrelevant alternatives criterion satisfied?

Answer 1

I can't open the table, but this looks like an illustration of Arrow's Voting Paradox. Arrow and Debreu won the Nobel Prize in economics for a mathematical proof that any social choice rule, such as democratic voting, violates fundamental axioms of rationality, concerning non-dictatorship, transitivity, irrelevant alternatives, and more.

the usual table of preferences has A>B>C, B>C>A, C>A>B, so that it just depends on what's on the ballot as society's preferences are not transitive. This comes up in close elections. if most all the rationality assumptions are valid, then some voter acts as the dictator.

there is a vast academic literature on Kenneth Arrow's Voting Paradox or Impossibility Theorem. as people look for ways around it and real life illustrations of its validity

One criticism is that it does not include intensity of preferences. There seems to be no way to capture how intensely a voter's preferences are. If half the country intensely wants candidate A, and the other half plus one voter are nearly unconcerned and just barely prefer candidate B, then B wins. Is that rational? and how to correct for it? One "correction" is make it harder to vote, so only the most intensely concerned voters, or more of them, decide the election. they also tend to be more informed, and having informed voters decide elections is better than having uncaring low info voters decide.