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.


3 thoughts on “A Voting Paradox

  1. “This is our present situation—there is no compromise and both parties fight for complete control at the expense of nearly half the country.”

    Neither party believes that it acts at the expense of half the country. Each is convinced that it knows what is best for everyone, regardless of what the voters want. But you don’t even have to be that cynical. Many politicians believe that taking office is a mandate from the voters themselves to fight for a full ideological agenda (I’m looking at you, new 2010 Republican Congressmen). They can even cite the polls to prove it! Well, some of them, anyway. The rest are simply propaganda from the other side.

    On the other hand, while the public may not get what it needs or even what it wants, it does get what it asks for, deliberately or indeliberately: ignorant, foolish, dishonest, selfish politicians with misplaced loyalties, if any. And it will get the same result as long as extremists dominate politics in one way or another, as long as bribe money flows freely into the pockets of politicians, as long as religion is substituted for science and reason in all significant discourse, as long as only a few know (or care to know in the first place) how the system works, as long as greed is glorified in all but name, and, of course, as long as the public acts out political tribalism.

  2. It seems like a fundamental flaw of a two-party system. But it’s a really tough situation because would a three party (or more) system be better? That would seem to make problems of the second kind even worse! Imagine (gods forbid) if the Evangelical right were the largest of several smaller parties.

  3. I have never been a fan of a 3+-party system. Why would we want to elect someone who might have no more than 34% popularity? Now, if elections consisted of multiple voting sessions such that the bottom few of each session are progressively eliminated from the competition until only two are left for the final showdown, we might have an improvement. We might not even need parties, though this system would have its own problems.

    Really, we can only tinker with our systems so much. Eventually, we have to admit that humanity as we know it is the problem, that its vices (particularly greed and pride) always find ways to manifest. I am convinced that our only realistic hope in the long run is through technology that alters us significantly on some fundamental level or greatly facilitates the satisfaction of our needs and desires. It is at least more realistic than the expectation that deregulation would effectively eliminate our problems, that the government will ever be able to protect us from ourselves or be free from corruption itself, or that we might each become a potential philosopher-king with the right education.

    On the other hand, we could do much worse than we have in the United States. I must always remind myself of this when I begin to criticize everything.

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