Voting Games: Part I
2. Voting systems and games
Most democracies use a direct system of translating voter feelings into the selection of a single winner (e.g. elections for U.S. Senator) or group of winners (e.g. members of a faculty search committee) for the election. However, for a variety of complex reasons, when the U.S. Constitution was created it did not call for the direct election of the President, but for an indirect system using an Electoral College. (Up until 1913, when the 17th Amendment went into effect, even Senators were not directly elected by the American people. They were "chosen" by state legislators.) Thus, strictly speaking, when Americans vote for president they are not voting for a candidate for president but rather for a statewide group of electors committed to voting for the candidate the voter chose. The number of these electors is equal to the total number of senators and members of the House of Representatives for that state. There are also electors for the District of Columbia.
Since the number of members each state has in the House of Representatives can change every 10 years, which reflects the number of seats assigned by the Huntington-Hill Method of Apportionment, the relative power of the states in the Electoral College can change with time. Furthermore, historically the electors who are selected for each state are chosen on a "winner take all" basis. Thus, if in Florida George Bush beat Albert Gore by a single vote in 2000, all of Florida's electors would have been committed to vote for George Bush. Technically, the issue of whom electors vote for is complex, too, and some states have experimented or are considering experimenting with dividing the number of electors between the candidates who run for president on the basis of the popular vote rather than using "winner take all."
In order to determine if a group of players has "won" the game or been able to achieve its goal, there is a number known as the quota associated with the game. Any group of players that casts blocks of votes, the sum of whose weights exceed the quota, "wins." In the Electoral College there are different groups of states such that if a candidate wins those states, the candidate will be elected president because the weights associated with these states exceed the required quota (270). Thus, the Electoral College is an example involving weighted voting. Sometimes the phrase "weighted voting game" is used. For the case of the Electoral College, weighted voting did not arise directly because of concern with equity issues. Some would argue that it arose for opposite reasons! However, let us look at a variety of settings where equity seems to be the driving force behind using voting games or weighted voting.
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