How do we chose democratically a president? Or the winner of a writing contest? Sounds trivial: we invite to vote all those who is allowed to. In truth there are different ways in which it is possible to vote and in which the votes can be measured which can lead to very different results.
The science that studies those techniques and their effect is the voting theory, topic of this chapter. Voting theory started being formally studied more than 200 years ago, during the French revolution when it was presented the problem of how to chose the best solution among the one presented among the participants to the assemblies. One of the most distinguished researcher on voting theory was the Marquis de Condorcet, who participated intensely to the debate on the new French Constitution before mysteriously dying in jail where he was locked up by the revolutionaries themselves. His legacy lives on like few other researchers, and we shall look at Condorcet system with great details as many eDemocratic system tend to use them.
Voting theory is divided into several branches:
1. The voting technique can relate to elect a major, a book, in any case a single winner. This is the field we shall investigate in this chapter.
2. It can instead be used to try to select a jury, this is the hypothesis multi-winner.
3. Or it can be used to try to select the participants in a Parliament. In some places this is the most debated part of the theory and most followed by media especially when a country is deciding if they should change their electoral vote. But it is not the only one, nor the most important. Notice how a Jury and a Parliament are generally considered differently.
4. And finally there is a fourth part of the theory which is budgeting when a group of people is trying to chose among a series of elements each which has a cost, and such that all together they don’t go over a certain limit. In this case there is a balance between the chosen elements because if the first winner is very costly there will be less resources available for the other winners.
We shall add a caveat: in the description of the voting theory in this chapter the choices are predetermined. Who is voting, thus, does not has the possibility to add other options, other candidates, other books to vote. This becomes very important when we are going to face the theme of eDemocracy where the options are not predetermined.