Resumen de Several ways of taking decisions by voting

Antonio Magaña, Francesc Carreras Escobar

• Usually, organisms that take decisions by voting are exclusively modeled in terms of simple games. Then, to measure the �power" of each player in the game/organism, some index of power (as the Shapley�Shubik or Banzhaf indices) is used.

  The problem is that the same organism does not always use the same procedure to take decisions and, so, simple games (and the power indices related to them) do not describe accurately enough the position of voters in the organism.

  Take, for instance, a Parliament: daily affairs are commonly decided by relative majority.

  In this work we study and compare different rules used in practice when voting. To make an appropriate description of relative majority rules, we use simple games with alternatives and the extension of the Shapley�Shubik and Banzhaf indices to this context. We apply these rules to an example: the País Vasco Parliament during the 2001�2005 Legislature.

  The different voting procedures that we analyze are:

  (a) Voting on a single motion when approval requires absolute majority.

  (b) Voting on a single motion when approval requires a qualified majority (greater than 1/2).

  (c) Voting on a single motion when approval requires relative majority.

  (d) Voting on two simultaneous motions when approval of any of them requires relative majority.

  To end the work, we discuss the situation that arises when a player announces its preferences before voting. In fact, the proposal that voters vote is presented for one (or more) of them and, consequently, this voter will vote for it.