Voting Paradox – Majority Out of Three


Is a majority vote out of three still a majority vote out of three if the first two votes are voiced and heard by all before the third vote is even cast?

If the first two votes make the majority (“yay and yay” or “nay and nay”) then the third voter knows there is no point to voting… he holds no influence and the problem reduces to one in which the decision is made if and only if it is unanimous between two people. Why then cast the third vote? If the third voter is in disagreement, perhaps his best course of action is to refrain from voting all together, in order to prevent the vote from closing and the decision from being implemented.

If he must cast a vote, however, he should vote contrary to the other two. Therefore, if the decision is good it is still enforced, and if the decision is bad he wont be blamed – he will in fact be appreciated for his forethought and insight.

Then, if the first two voters give different votes… then the third voter is the deciding vote and he holds all the power. Essentially, the first two voters are abstaining from vote entirely and just letting the third guy make the sole decision. If the third voter knows he is the deciding factor, does he not bare sole responsibility for the outcome of the decision?

Does this line of reasoning seem reasonable? Is it a legitimate paradox of reason, a cognitive paradox? Or is it just my own confusion and fallacy?

It seems to me just because there are three voters, and for each their vote is weighted the same, doesn’t equivocally mean the vote is democratic and fair. Its an unusual phenomenon, perhaps, but doesn’t exist solely on paper – I perceive it in reality as well during any electoral vote. The television will announce the victors of certain collages and states to other states during the election process, and conceivably altering other peoples votes (at least for the nations and committees in which tallying begins prior to the end of the voting process, not relevant for all countries).

You may argue that on a grander scale the influence is insignificant. Perhaps that is true, but existent nonetheless. Is any degree of unfairness any less unfair than the hypothetical fairness it should be?

You may also argue that on the small scale of three voters, whether or not the third voter has all or no influence is determined by the first two votes, and therefore the possibilities nullify – that on average the third voter has just as much influence as the other two. I disagree. The third voter always has all or none of the power. The third voters degree of influence is never average or on par.

The argument that the third voters influence is average in the long run is a statistical fallacy. I’m reminded of the three statisticians hunting a deer. The first misses left, the second misses right, and the third lowers his gun and says “we hit it”. Obviously having the choice of two extremes never averages to somewhere in between.

In order to be truly democratic, it seems, the best course of action is to obscure all votes from all voters until all votes have been cast… then and only then tally them up and reveal the results.

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