Analysis of information sources in references of the Wikipedia article "Condorcet paradox" in English language version.
83.1% … 97.9% … 98.8% … Figure 2: Frequency of CWs and weak CWs with an increasing number of voters
Here, Condorcet notes that we have a 'contradictory system' that represents what has come to be known as Condorcet's Paradox.
it is widely acknowledged that the impartial culture is unrealistic ... the impartial culture is the worst case scenario
most election results do not correspond to anything like any of DC, IC, IAC or MC ... empirical studies ... indicate that some of the most common paradoxes are relatively unlikely to be observed in actual elections. ... it is easily concluded that Condorcet's Paradox should very rarely be observed in any real elections on a small number of candidates with large electorates, as long as voters' preferences reflect any reasonable degree of group mutual coherence
small departures of the impartial culture assumption may lead to large changes in the probability of the paradox. It may lead to huge declines or, just the opposite, to huge increases.
to have a PMRW with probability approaching 15/16 = 0.9375 with IAC and UC, and approaching 109/120 = 0.9083 for MC. … these cases represent situations in which the probability that a PMRW exists would tend to be at a minimum … intended to give us some idea of the lower bound on the likelihood that a PMRW exists.
Mean number of voters: 1000 … Spatial model: 99.47% [0.5% cycle likelihood] … 716.4 [ERS data] … Observed elections: 99.32% … 1,566.7 [ANES data] … 99.56%
There are many Condorcet methods, which vary primarily in how they deal with ties, which are very common when a Condorcet winner does not exist.
Here, Condorcet notes that we have a 'contradictory system' that represents what has come to be known as Condorcet's Paradox.
it is widely acknowledged that the impartial culture is unrealistic ... the impartial culture is the worst case scenario
small departures of the impartial culture assumption may lead to large changes in the probability of the paradox. It may lead to huge declines or, just the opposite, to huge increases.
to have a PMRW with probability approaching 15/16 = 0.9375 with IAC and UC, and approaching 109/120 = 0.9083 for MC. … these cases represent situations in which the probability that a PMRW exists would tend to be at a minimum … intended to give us some idea of the lower bound on the likelihood that a PMRW exists.
Mean number of voters: 1000 … Spatial model: 99.47% [0.5% cycle likelihood] … 716.4 [ERS data] … Observed elections: 99.32% … 1,566.7 [ANES data] … 99.56%
Clearly, if anyone's vote was self-contradictory (having cyclic preferences), it would have to be discounted, and we should therefore establish a form of voting which makes such absurdities impossible
Here, Condorcet notes that we have a 'contradictory system' that represents what has come to be known as Condorcet's Paradox.
it is widely acknowledged that the impartial culture is unrealistic ... the impartial culture is the worst case scenario
most election results do not correspond to anything like any of DC, IC, IAC or MC ... empirical studies ... indicate that some of the most common paradoxes are relatively unlikely to be observed in actual elections. ... it is easily concluded that Condorcet's Paradox should very rarely be observed in any real elections on a small number of candidates with large electorates, as long as voters' preferences reflect any reasonable degree of group mutual coherence
small departures of the impartial culture assumption may lead to large changes in the probability of the paradox. It may lead to huge declines or, just the opposite, to huge increases.
to have a PMRW with probability approaching 15/16 = 0.9375 with IAC and UC, and approaching 109/120 = 0.9083 for MC. … these cases represent situations in which the probability that a PMRW exists would tend to be at a minimum … intended to give us some idea of the lower bound on the likelihood that a PMRW exists.
There are many Condorcet methods, which vary primarily in how they deal with ties, which are very common when a Condorcet winner does not exist.
