Intuition about voting is that vote share is proportational to voting power. For example someone holding two votes have a larger say in decisions than the others each holding only one. But this larger say is a rather vague concept, making it hard to measure boundary cases where quantity and quality become more meddled together. This is where science comes in, and probability is introduced to capture the indeterministic nature of voting game equilibrium.
While the central interest is in measuring the power distribution in such games, the setting is formulated as one where power is measured ceteris paribus, i.e. whether the change in one voter's decision can alter the voting result when all others's votes are being held fixed, and how frequent this can be the case, which frequency is interpreted as power, since others will try to form coalition with the more decisive voter which gives the person power in social interactions. Voting share alone cannot really capture power since it presumes an individualistic social structure and in most cases no single person can have a larger than threshold voting share directly and thus one-handedly make decisions in a modern voting system.
The ceteris paribus setting is slightly different from that in general game and equilibrium theories, where others' votes are also being held fixed, but it is the exact choice of the last person rather than the relationship between this choice and the final result that is being investigated.
While the central interest is in measuring the power distribution in such games, the setting is formulated as one where power is measured ceteris paribus, i.e. whether the change in one voter's decision can alter the voting result when all others's votes are being held fixed, and how frequent this can be the case, which frequency is interpreted as power, since others will try to form coalition with the more decisive voter which gives the person power in social interactions. Voting share alone cannot really capture power since it presumes an individualistic social structure and in most cases no single person can have a larger than threshold voting share directly and thus one-handedly make decisions in a modern voting system.
The ceteris paribus setting is slightly different from that in general game and equilibrium theories, where others' votes are also being held fixed, but it is the exact choice of the last person rather than the relationship between this choice and the final result that is being investigated.
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