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

question 9

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.
-Given the preference orderings listed above, what would the result be of a pair-wise contest between the spending choices education and medical?

• A) education
• B) medical
• C) tax cut
• D) it would be a tie

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Definitions:

Unbiased Coins

A theoretical or actual coin for which the probability of landing heads or tails is equal, exemplifying a fair probability scenario in random experiments.

Simple Events

Events that cannot be broken down into smaller parts and have a single outcome.

Simple Events

Events that cannot be broken down into simpler components within the context of probability.

Events

An occurrence or happening, especially one significant in terms of a statistical analysis or probability calculation.