Intransitivity

From Academic Kids

Intransitivity is a scenario in which weighing several options produces a "loop" of preference.

Such as:

  • A is preferred to B
  • B is preferred to C
  • C is preferred to A

Generally, a binary relation is transitive if "A is related to B" and "B is related to C" necessitates "A is related to C". For example, the "more than" relation is transitive", and the "lives in the same county as" relation is transitive. See transitive relation.

Intransitivity can occur in analysis of probabalistic outcomes in game theory and in the Condorcet voting method in which ranking several candidates can produce a loop of preference when the weights are compared. Another well known example is the children's game rock, paper, scissors.

Likelihood of intransitivity

It has been sugested that Condorcet voting tends to eliminate "intransitive loops" when large numbers of voters participate because the overall assessment criteria for voters balances out. For instance, voters may prefer candidates on several different units of measure such as by order of social consciousness or by order of most fiscally conservative.

(SciAm Feb/Apr 2004?)

In such cases intransitivity reduces to a broader equation of numbers of people and the weights of their units of measure in assessing candidates.

Such as:

  • 30% favor 60/40 weighting between social consciousness and fiscal conservatism
  • 50% favor 50/50 weighting between social consciousness and fiscal conservatism
  • 20% favor a 40/60 weighting between social consciousness and fiscal conservatisim

While each voter may not assess the units of measure identically, the trend then becomes a single vector on which the consensus agrees is a preferred balance of candidate criteria.

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