Utilitarian Collective Choice and Voting

In his seminal Social Choice and Individual Values, Kenneth Arrow
stated that his theory applies to voting. Many voting theorists
have been convinced that, on account of Arrow’s theorem, all voting
methods must be seriously flawed. Arrow’s theory is strictly
ordinal, the cardinal aggregation of preferences being explicitly
rejected. In this paper I point out that all voting methods are
cardinal and therefore outside the reach of Arrow’s result.
Parallel to Arrow’s ordinal approach, there evolved a consistent
cardinal theory of collective choice. This theory, most prominently
associated with the work of Harsanyi, continued the older
utilitarian tradition in a more formal style. The purpose of this
paper is to show that various derivations of utilitarian SWFs can
also be used to derive utilitarian voting (UV). By this I mean a
voting rule that allows the voter to score each alternative in
accordance with a given scale. UV-k indicates a scale with k
distinct values. The general theory leaves k to be determined on
pragmatic grounds. A (1,0) scale gives approval voting. I prefer
the scale (1,0,-1) and refer to the resulting voting rule as
evaluative voting. A conclusion of the paper is that the defects of
conventional voting methods result not from Arrow’s theorem, but
rather from restrictions imposed on voters’ expression of their
preferences. The analysis is extended to strategic voting,
utilizing a novel set of assumptions regarding voter behavior.