are either above or below the cutoff, the voter votes for all or none of the candidates, despite preferring some over others. This could be imagined to reflect a case where many voters become disenfranchised and apathetic if they see no candidates they approve of. In a case such as this, many voters may have an internal cutoff, and would not simply vote for their top 3, or the above average candidates, although that is not to say that it is necessarily entirely immovable. For example, in this scenario, voters are voting for candidates with approval above 50% (bold signifies that the voters voted for the candidate): C wins with 65% of the voters' approval, beating B with 60%, D with 40% and A with 35% If voters' threshold for receiving a vote is that the candidate has an above average approval, or they vote for their two most approved of candidates, this is not a dichotomous cutoff, as this can change if candidates drop out. On the other hand, if voters' threshold for receiving a vote is fixed (say 50%), this is a dichotomous cutoff, and satisfies IIA as shown below: B now wins with 60%, beating C with 55% and D with 40% With dichotomous cutoff, C still wins. B now wins with 70%, beating C and A with 65% With dichotomous cutoff, C still wins. Compliance with voting system criteria Most of the mathematical criteria by which voting systems are compared were formulated for voters with ordinal preferences. In this case, approval voting requires voters to make an additional decision of where to put their approval cutoff (see examples above). Depending on how this decision is made, approval voting satisfies different sets of criteria. There is no ultimate authority on which criteria should be considered, but the following are criteria that many voting theorists accept and consider desirable: Unrestricted domain—A voter may have any preference ordering among the alternatives. Non-dictatorship—There does not exist a single voter whose preference for the alternatives always determines the outcome regardless of other voters' preferences. Pareto efficiency—If every voter prefers candidate A to all other candidates, then A must be elected. (from Arrow's impossibility theorem) Majority criterion—If there exists a majority that ranks (or rates) a single candidate higher than all other candidates, does that candidate always win? Monotonicity criterion—Is it impossible to cause a winning candidate to lose by ranking that