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Table 22-2 Three Longtime Friends-Fred,Barney,and Wilma-Are Deciding How They Will Spend Their

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Table 22-2
Three longtime friends-Fred,Barney,and Wilma-are deciding how they will spend their Sunday afternoon.They all agree that they should do one of three things: go to a movie,go to the beach,or go to a museum.They also agree that they will have two pairwise votes to determine how to spend their evening,with the majority determining the outcome on each vote.The first,second,and third choices for each person are as indicated in the table below.
Table 22-2 Three longtime friends-Fred,Barney,and Wilma-are deciding how they will spend their Sunday afternoon.They all agree that they should do one of three things: go to a movie,go to the beach,or go to a museum.They also agree that they will have two pairwise votes to determine how to spend their evening,with the majority determining the outcome on each vote.The first,second,and third choices for each person are as indicated in the table below.    -Refer to Table 22-2.Which of the following statements is correct regarding the Condorcet paradox and the results of pairwise voting by Fred,Barney,and Wilma? A)  The paradox implies that pairwise voting never produces transitive preferences,and so the voting by Fred,Barney,and Wilma fails to produce transitive preferences. B)  The paradox implies that pairwise voting sometimes (but not always) produces transitive preferences,and the voting by Fred,Barney,and Wilma does produce transitive preferences. C)  The paradox implies that pairwise voting sometimes (but not always) fails to produce transitive preferences,and the voting by Fred,Barney,and Wilma fails to produce transitive preferences. D)  The paradox does not apply to the case at hand,because Barney's preferences are not individually transitive.
-Refer to Table 22-2.Which of the following statements is correct regarding the Condorcet paradox and the results of pairwise voting by Fred,Barney,and Wilma?

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Definitions:

Payoff Matrix

A table that shows the potential outcomes or payoffs in a decision-making situation, typically used in game theory to analyze the strategies of different players.

Dominant Strategy

In game theory, a strategy that yields the best outcome for a player, regardless of what the other players do.

Nash Equilibrium

An idea in game theory that suggests no participant can gain an advantage by altering their approach if all other participants maintain their strategies.

Payoff Matrix

A tabular representation of the payoffs or outcomes in a strategic game for each set of strategies chosen by the players.

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