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In social choice theory, Condorcet's voting paradox is a fundamental discovery by the Marquis de Condorcet that majority rule is inherently self-contradictory.The result implies that it is logically impossible for any voting system to guarantee that a winner will have support from a majority of voters: for example there can be rock-paper-scissors scenario where a majority of voters will prefer ...
Social choice theory is the study of theoretical and practical methods to aggregate or combine individual preferences into a collective social welfare function. The field generally assumes that individuals have preferences , and it follows that they can be modeled using utility functions , by the VNM theorem .
Arrow's impossibility theorem is a key result in social choice theory, ... (notice that it is the cyclic voting pattern which causes the Condorcet paradox):
A Condorcet winner may not necessarily always exist in a given electorate: it is possible to have a rock, paper, scissors-style cycle, when multiple candidates defeat each other (Rock < Paper < Scissors < Rock). This is called Condorcet's voting paradox, [6] and is analogous to the counterintuitive intransitive dice phenomenon known in ...
In social choice theory, the best-is-worst paradox occurs when a voting rule declares the same candidate to be both the best and worst possible winner. The worst candidate can be identified by reversing each voter's ballot (to rank candidates from worst-to-best), then applying the voting rule to the reversed ballots find a new "anti-winner".
Example Condorcet method voting ballot. Blank votes are equivalent to ranking that candidate last. A Condorcet method (English: / k ɒ n d ɔːr ˈ s eɪ /; French: [kɔ̃dɔʁsɛ]) is an election method that elects the candidate who wins a majority of the vote in every head-to-head election against each of the other candidates, whenever there is such a candidate.
Discursive dilemma or doctrinal paradox is a paradox in social choice theory. The paradox is that aggregating judgments with majority voting can result in self-contradictory judgments. Consider a community voting on road repairs asked three questions; the repairs go ahead if all three answers are 'Yes'.
Condorcet and his contemporary Laplace demonstrated that, in such a model, voting theory could be reduced to probability by finding the expected quality of each candidate. [2] The jury model implies several natural concepts of accuracy for voting systems under different models: