ORDINALS, CARDINALS, AND POLITICS

The burgeoning protests across the country triggered by Wisconsin governor Walker's assault on the right of public employees to bargain collectively remind me once again of the importance, for an understanding of American politics, of the distinction between ordinal and cardinal preference orders. For those of you who did not read my Formal Methods blog, and have not familiarized yourselves with that material in other ways, let me say briefly that an ordinal preference order establishes a person's ranking across a set of available alternatives that encodes only the information that, as between any two alternatives, the person either prefers the first to the second, or prefers the second to the first, or is indifferent between them. A consistent ordinal preference order is transitive: If one alternative is preferred to a second, and that second to a third, then the first is preferred to the third. Rankings are said to be incomplete when not every possible pair is ranked. A cardinal preference order encodes not only the order of preference but also, speaking informally, the intensity of that preference. A simple example should make this clear. Presented in the 1992 election, as most of us were, with ballots listing three candidates for president -- Bush, Clinton, and Perot -- it is easy to imagine that among voters who preferred Clinton to Perot and Perot to Bush, some preferred Clinton much more than either Bush or Perot, but preferred Perot marginally to Bush, while others were torn between Clinton and Perot, both of whom they much preferred to Bush, but in the end opted for Perot. The ordinal rankings of both groups of voters were identical -- namely Clinton > Perot > Bush -- but the cardinal rankings were dramatically different.

Wikipedia tells us that there are thirty-two countries that require their citizens to vote, though only twelve enforce the requirement [Australia, Singapore, Chile, and Lichtenstein, among others.] Under such a rule, the distinction between ordinal and cardinal rankings is irrelevant. The two rankings will produce identical results in an election. But in the United States, which does not enforce voting even for registered voters, who are only a fraction of the pool of eligible voters, intensity of preference is frequently the whole game. As I have remarked on this blog before, only 60% or so of eligible voters vote in a presidential year, and scarcely a third in off years, so turnout, driven by intensity of preference, determines the outcome of most elections.

In the past year and a half, all of the intensity has been on the extreme right -- hence the disastrous off-year election. But quite unexpectedly, the Republicans have overreached, in Wisconsin and elsewhere, with the result that the balance of intensity of preference has shifted. I confess that I would not have expected so local an issue as union collective bargaining rights in Wisconsin to arouse the slumbering beast of left-of-center voters, but it has, and at this point it is very difficult to tell what the consequences will be for the next election cycle.

All those of us on the sidelines can do is cheer, give money, sign petitions, perhaps attend rallies [not my favorite thing to do], and hope that the Republicans continue to misjudge the temper of the electorate.