math ch. 2

voting system in which some voters have more votes than others, i.e. some votes carry more weight ex: electoral college - different states have differing amounts of electoral votes

votes of yes or no for some decision

the voters who may no longer be individuals (could be states, corporations, governments, etc.)

the number of total weights needed to pass a motion

when groups in a weighted voting system can each meet the quota in a tie; the the quota requirement is less than simple majority, there is potential for both sides of an issues to win

when the quota can never be met and no motion can ever pass; quota is more than the total number of votes in the system

a quota outside the _____ of possible values leads to anarchy (if q is too low) or gridlock (if q is too high) V/2 < q <_ V

a player who can single-handedly control the outcome of an election, with the other players having no say; weight is bigger than or equal to the quota

the players with no say under a dictator

a player has this if a motion cannot pass without them; cannot force a motion to pass, but can force it to fail

how much power a player has in a vote may not be obvious based solely on that player's weight; tells you which player has the most sway (power) in the most elections / biggest slice of the "power pie" 1. list all coalitions possible and mark the winning ones 2. for a player P1 count the # of times P1 is critical in a winning coalition (call that # B1) 3. repeat for all players 4. sum all critical counts (T= B1+B2+...BN) 5. find BPI for P1 -> ~B1= B1/T

any set of players who "join forces" and vote alike

a player in a coalition whose vote is necessary for that coalition to win

another method for determining power; uses the assumption that votes are cast one at a time, meaning that coalitions are formed sequentially, and the order that players join a coalition does make a difference

coalition in which the order of players matters (P1, P2) = (P2, P1) but IS NOT =

the player in a sequential coalition whose vote pushes the coalition "over the edge" into winning; there is only one in each winning coalition

if we have 2 consecutive independent decisions to make with c choices for decision 1 and d choices for decision 2, then there are c * d choices possible overall

notation M! means m * (m-1) * (m-2) * ... 3 * 2 * 1 1! = 1 0! = 1 N! gets very large very fast as N grows so SSPI is not practical for large N