Unlike personal value scales, the outcomes of majority-voting procedures do not necessarily exhibit transitivity and hence cannot always be represented as orderings (cf. "Details" box on p. 1.3:17). Suppose, for example, that with regard to a certain political issue, alternatives A, B, and C are presented in public discussion. The electorate of 30 million voters is divided in their relative preferences among these alternatives. In fact, they divide into three approximately equal groups X, Y, and Z. As illustrated in the chart, all the voters in category X regard A as the best alternative and B as second best. Voters in category Y, however, would most like to see alternative C implemented, but would we willing to settle for A as the next best solution. But the Z voters see A as the worst alternative and B as the best.

X
10 million
voters

Y
10 million
voters

Z
10 million
voters

If all three alternatives were placed on the ballot, the electorate would be evenly divided. More typically in real-life elections, however, voters confront two principal choices. For instance, under a two-party system, one candidate might espouse alternative A, while the other supports B. If this choice is the election's major deciding issue, then the X and Y voters both prefer A to B, so that the candidate supporting A will win by a landslide, with 2/3 of the total votes.

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