Distributed Score Voting: Difference between revisions

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Graphically, each candidate is a node; the head-to-head is represented by an arrow, leaving the winning candidate, entering the losing candidate. The tie is represented as a double arrow entering, that is both candidates are considered losers.

2) Find the smallest set X (Smith set) of nodes that don’t have incoming arrows, coming from outside the set.

2) Find the smallest set X ([[Smith set]]) of nodes that don’t have incoming arrows, coming from outside the set.

Then remove all candidates not in X from the votes.

3) Convert the votes into a range form, assigning 0 points to the candidates with the lowest score and normalizing* the remaining candidates, using the following formula:

3) Convert the votes into a range form, assigning 0 points to the candidates with the lowest score and normalizing the remaining candidates, using the following formula:

M = candidate with the highest score, before normalization.

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By repeating this process several times, you can get as many winners as you like, which will be those removed in point 5.

6) If you want to know the % of victory of the winning candidates then, in each original vote, you must remove all the candidates who haven’t won, and normalize* the vote with the formula used in point 3 (with W=100 fixed). The sum of points for each candidate will indicate the % of victory.

6) If you want to know the % of victory of the winning candidates then, in each original vote, you must remove all the candidates who haven’t won, and normalize the vote with the formula used in point 3 (with W=100 fixed). The sum of points for each candidate will indicate the % of victory.

===Head-to-head===

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Criteria met by DSV:

* Majority criterion

*[[Majority criterion]]

* Majority loser criterion

*[[Majority loser criterion]]

* Mutual majority criterion

*[[Mutual majority criterion]]

* Condorcet criterion

*[[Condorcet criterion]]

* Condorcet loser criterion

*[[Condorcet loser criterion]]

* Smith criterion

*[[Smith criterion]]

* Independence of irrelevant alternatives

*[[Independence of irrelevant alternatives]]

* Independence of clones criterion

*[https://en.wikipedia.org/wiki/Independence_of_clones_criterion Independence of clones criterion]

* Monotonicity criterion

*[[Monotonicity criterion]]

* Reversal symmetry

*[https://en.wikipedia.org/wiki/Reversal_symmetry Reversal symmetry]

* Pareto criterion

*[[Pareto criterion]]

Criteria not met by DSV:

* Participation criterion

*[[Participation criterion]]

* Consistency criterion

*[[Consistency criterion]]

* Later-no-harm criterion

*[[Later-no-harm criterion]]

* Later-no-help criterion

*[[Later-no-help criterion]]

* Favorite betrayal criterion

*[[Favorite betrayal criterion]]

The first two criteria not met are derived mainly from the fact that DSV wants to ensure the victory of the candidate who wins all the head-to-head (when it exists).

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This type of tactical vote works only if:

* there is a ~~condorcet~~ paradox which includes at least 4 candidates.

* there is a [[Condorcet paradox]] which includes at least 4 candidates.

* through the tactical vote, the candidate who should have been the winner can be taken out of the Smith set.

* through the tactical vote, the candidate who should have been the winner can be taken out of the [[Smith set]].

* the new winner is actually a better candidate than the previous one (the new winner in the example could also be C).

* the voter has a fairly precise knowledge of the likely ballots result, without which this tactical vote would turn against him.