Symmetry of simple games and permission of voters

In this paper, we deal with symmetry of voting situations with voters' permission. The situations are expressed by committees with permission, and are investigated focusing on the simple games induced by the committees, that is, permission games and restricted permission games. Particularly, we examine relations between classical concept of symmetry of simple games and voters' permission, and provide propositions that allow us to regard classical symmetric simple games as situations with the assumption that the voters in each winning coalition can agree on at least one alternative.