On 27.7.2011, at 22.50, Toby Pereira wrote: > Very simple case - two voters and two candidates. Candidate A get scores of > 0/10 and 10/10. Candidate B gets 5/10 and 5/10. Under normal range voting, it > would be a draw. But to me, candidate B seems the much fairer choice.
Different choices and elections may well have different criteria on which choice is the best and should be chosen. Sometimes one may want to maximize the sum of happiness, but sometimes one maybe wants to maximize the worst outcome to the voters. One could also have a mixture of those approaches. If I plan to share a pizza with my friend we might think that first of all that the choice we make should not be unpleasant to neither one of us. That means that we want to maximize the worst result to some acceptable level. Let's say anything under 5 would not be nice. But after that it could be ok to allow one of us to just pick the pizza that he strongly wants, if that just doesn't cause any major problems to the other. That means that result 10/10 and 5/10 could be better than 7/10 and 7/10 (although 5/10 and 0/10 could be worse than 2/10 and 2/10). One could also have elections / decisions where the voters do not use the full range but just a smaller segment of it, thereby intentionally allowing others to have more influence on the outcome. One could allow also ratings from minus infinity (-oo) to plus infinity (oo). In that model rating -oo would mean a veto to that alternative. Rating oo means that the voter demands that alternative to be chosen. If some candidate gets both -oo and oo, then the result is not defined (the election is undecided). The result is also undecided if two different alternatives will get oo. Another approach to the original problem is that voters could actually take the impact to others into account when they evaluate the alternatives. If I know that my friend is allergic to fish I might rate a fish pizza at 0 although I myself would find it worth 8 if I would eat alone. Some other person might decide to maximize their own interests and never mind others. Both approaches would be ok in this model. My point is just that there can be many kind of needs and elections, depending on what kind of outcome one wants and how one expects and tells the voters to vote. The most common environment that the methods are planned for is a competitive political environment where majority decisions are the norm. But that does not mean that all elections / decisions and methods should follow the same pattern. Juho
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