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

question 21

Multiple Choice

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

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Definitions:

Registered Democrats

People who are officially enrolled as Democratic Party members with voting rights in the United States.

Registered Republicans

Individuals officially registered to vote as members of the Republican Party in the United States.

Pooled Variance T-test

A statistical test that combines the variances of two samples to test the hypothesis that the means of two populations are equal under the assumption of equal variances.

Degrees Of Freedom

The number of independent pieces of information in a dataset available for estimating parameters or calculating a statistic, usually defined as the number of observations minus the number of parameters being estimated.