Imagine that three city council members are trying to decide how to spend a surplus. The options currently being debated are (i) spend it on improving primary education in the municipality, (ii) spend it on improving the level of medical care offered by the local hospital, or (iii) lower local taxes and use the surplus to cover the costs of existing programs. The council employs majority rule to make its decisions. The councillors have the following preference orderings over the spending choices:
Councillor 1: Education $\succ$ Medical $\succ$ Tax cut
Councillor 2: Medical $\succ$ Tax cut $\succ$ Education
Councillor 3: Tax cut $\succ$ Education $\succ$ Medical
Assume that the councillors hold a round-robin tournament that pits each alternative against every other alternative in a series of pair-wise votes. The winner is the alternative that wins the most contests. Based on this information, answer the following four questions.
-Which of the outcomes, if any, is a Condorcet winner?
A) education
B) medical
C) tax cut
D) there is no Condorcet winner in this example

Question

Imagine that three city council members are trying to decide how to spend a surplus. The options currently being debated are (i) spend it on improving primary education in the municipality, (ii) spend it on improving the level of medical care offered by the local hospital, or (iii) lower local taxes and use the surplus to cover the costs of existing programs. The council employs majority rule to make its decisions. The councillors have the following preference orderings over the spending choices: 
Councillor 1: Education $\succ$ Medical $\succ$ Tax cut
Councillor 2: Medical $\succ$ Tax cut $\succ$ Education
Councillor 3: Tax cut $\succ$ Education $\succ$ Medical 
Assume that the councillors hold a round-robin tournament that pits each alternative against every other alternative in a series of pair-wise votes. The winner is the alternative that wins the most contests. Based on this information, answer the following four questions.
-Which of the outcomes, if any, is a Condorcet winner?
A) education
B) medical
C) tax cut
D) there is no Condorcet winner in this example

Quizplus · Accepted Answer

A Condorcet winner is an option that can win against every other option in a head-to-head comparison. In this scenario, each option wins one contest and loses another, meaning no single option is preferred over all others by a majority in every comparison. Education beats Medical (Councillor 1 and 3 prefer Education over Medical), Medical beats Tax Cut (Councillor 1 and 2 prefer Medical over Tax Cut), and Tax Cut beats Education (Councillor 2 and 3 prefer Tax Cut over Education), resulting in a cycle without a clear winner.

Imagine That Three City Council Members Are Trying to Decide ≻\succ≻

Imagine That Three City Council Members Are Trying to Decide $\succ$