Simultaneous and sequential voting under general decision rules

In an economic theory of voting, voters have positive or negative costs of voting in favor of a proposal and positive or negative benefits from an accepted proposal. When votes have equal weight then simultaneous voting mostly has a unique pure strategy Nash equilibrium which is independent of benefits. Voting with respect to (arbitrarily small) costs alone, however, often results in voting against the 'true majority' . If voting is sequential as in the roll call votes of the US Senate then, in the unique subgame perfect equilibrium, the 'true majority' prevails. It is shown that the result for sequential voting holds also with different weights of voters (shareholders), with multiple necessary majorities (European Union decision-making), or even more general rules. Simultaneous voting in the general model has more differentiated results.