Stalin once (supposedly) said that “He who casts the votes determines nothing; he who counts the votes determines everything “ But he was being insufficiently cynical. He who chooses the voting system may determine just as much as the other two players.

The Art of Strategy gives some good examples of this principle: here's an adaptation of one of them. Three managers are debating whether to give a Distinguished Employee Award to a certain worker. If the worker gets the award, she must receive one of two prizes: a $50 gift certificate, or a $10,000 bonus.

One manager loves the employee and wants her to get the $10,000; if she can't get the $10,000, she should at least get a gift certificate. A second manager acknowledges her contribution but is mostly driven by cost-cutting; she'd be happiest giving her the gift certificate, but would rather refuse to recognize her entirely than lose $10,000. And the third manager dislikes her and doesn't want to recognize her at all - but she also doesn't want the company to gain a reputation for stinginess, so if she gets recognized she'd rather give her the $10,000 than be so pathetic as to give her the cheap certificate.

The managers arrange a meeting to determine the employee's fate. If the agenda tells them to vote for or against giving her an award, and then proceed to determine the prize afterwards if she wins, then things will not go well for the employee. Why not? Because the managers reason as follows: if she gets the award, Manager 1 and Manager 3 will vote for the $10,000 prize, and Manager 2 will vote for the certificate. Therefore, voting for her to get the award is practically the same as voting for her to get the $10,000 prize. That means Manager 1, who wants her to get the prize, will vote yes on the award, but Managers 2 and 3, who both prefer no award to the $10,000, will strategically vote not to give her the award. Result: she doesn't get recognized for her distinguished service.

But suppose the employee involved happens to be the secretary arranging the meeting where the vote will take place. She makes a seemingly trivial change to the agenda: the managers will vote for what the prize should be first, and then vote on whether to give it to her.

If the managers decide the appropriate prize is $10,000, then the motion to give the award will fail for exactly the same reasons it did above. But ...

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