Consistency criterion

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A voting system is consistent if, when the electorate is divided arbitrarily into two (or more) parts and separate elections in each part result in the same choice being selected, an election of the entire electorate also selects that alternative. Smith[1] calls this property separability and Woodall[2] calls it convexity.

It has been proven a preferential voting system is consistent if and only if it is a positional voting system.[3]

The failure of the consistency criterion can be seen as an example of Simpson's paradox.

[edit] Reference

  1. ^ John H Smith, "Aggregation of preferences with variable electorate", Econometrica, Vol. 41 (1973), pp. 1027–1041.
  2. ^ D. R. Woodall, "Properties of preferential election rules", Voting matters, Issue 3 (December 1994), pp. 8–15.
  3. ^ H. P. Young, "Social Choice Scoring Functions", SIAM Journal on Applied Mathematics Vol. 28, No. 4 (1975), pp. 824–838.
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