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.

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.判断题

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