A Voting Paradox

Elizabeth Anscombe, in The Frustration of the Majority by the Majority’s Will, points out a clever paradox of voting. The issue is essentially that the majority of the people do not get what they want a majority of the time. Consider the following chart from Anscombe’s original article:


Voters A through K cast ‘yes’ or ‘no’ votes on 11 issues. Every issue passes by a margin of 6-5. But seven of the voters, A through G, voted ‘no’ on most issues (7/11). So, most people are not, in general, getting what they want.

This is meant to undermine the idea of democracy as ‘majority rule’. The majority may be ruling each specific issue, but that does not necessarily mean that most people will walk away from the process satisfied. This is not an unrealistic scenario. Let’s say the issues are tax increases and four people stand to benefit from many of these increases. This could explain the high rate of ‘yes’ votes from the four participants (H through K) benefitting from most of the outcomes.

I agree that this is an intriguing paradox that ought to make us seriously consider how a democracy is really supposed to work, but what has arisen to prevent such frustration of wills may be even worse. Consider how Congressional voting is done in the United States today. On most issues that are controversial, the two main parties form strict voting blocks. They stand together completely in order to throw as much weight behind an issue as possible. In this scenario, the majority should always carry the vote (of course, to make this completely successful, there must be an alignment of House, Senate, and President). We then see scenarios like the following:

Here, we have the majority’s will being satisfied, but at the total expense of the slight minority. We have 60% of the voting population fulfilling their will completely, while an entire 40% of the voting population’s will is thwarted completely. This seems altogether worse than the first scenario! This is our present situation—there is no compromise and both parties fight for complete control at the expense of nearly half the country.


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