Mark the statement below true if that statement is always true and false otherwise

A minimal winning coalition in a given simple game is defined as a coalition such that if any player leaves it, the coalition becomes losing or blocking.

Question

Mark the statement below true if that statement is always true and false otherwise

A minimal winning coalition in a given simple game is defined as a coalition such that if any player leaves it, the coalition becomes losing or blocking.

BlackTom AI · Accepted Answer

The question asks us to assess whether the given statement about minimal winning coalitions is always true.
Option 1: True. This would claim that a minimal winning coalition remains winning under all circumstances except when a member leaves, in which case it becomes blocking. In standard cooperative game theory, a minimal winning coalition is defined as a coalition that is winning, and if any single member leaves, the coalition becomes losing. It does not include the idea that the coalition would become blocking when a member exits. This makes the statement as a whole incorrect.
Option 2: False. The precise definition of a minimal winning coalition is that it is winning, and removing any one member makes it losing. There is no requirement or typical implication that removing a member turns it into a blocking coalition. A blocking coalition is conceptually different from a losing coalition, as blocking relates to preventing a passage under certain voting rules, whereas losing means the coalition lacks enough members to meet the quota. Therefore, equating the consequence of a member leaving to either losing or blocking is inaccurate, making the statement false.

In summary, the only accurate interpretation is that removing any member from a minimal winning coalition yields a losing coalition, not a blocking one, which is why the statement as written is false.

VPM Spring 2025 VPM Practice Final

Mark the statement below true if that statement is always true and false otherwise A minimal winning coalition in a given simple game is defined as a coalition such that if any player leaves it, the coalition becomes losing or blocking.

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