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) Is the head-to-head criterion satisfied?

Answer 1

This looks suspiciously like an example used in Arrow's Voting Paradox

or Impossibility Theorem

to show no social choice rule can satisfy basic axioms of rationality

such as transitivity

ABC

BCA

CAB

if it's AvB A wins

if it's BvC B wins

if it's CvA C wins

so it's just a matter of

who gets on the ballot that determines who wins

even though there is no social preference for any one candidate

this seems to happen sometimes in close elections or primaries

where one candidate wins in some states, another in other states

and a 3rd candidate wins in remaining states

leaving no clear winner

until the smoke filled rooms clear and they make a back room deal

although no table is shown, so it's unclear what the problem is about

Kenneth Arrow cowon a Nobel Prize for his proof of the public or social choice problems

a vast academic literature commented on his proof, endless articles and books on the subject