On the manipulability of votes
This is the first installment in a series about social choice and welfare. The structure will be: historical anecdote, followed by “spoon-feeding” the conclusions.
So, here go:
We are in the 1st century A.C.. Pliny the younger is the current “chairman” of the Roman Senate. And he is faced with a difficult situation. Consul Africius Dexter was found dead. Was he murdered? Was it an assisted suicide?
The freedmen who worked on his estate are sent to trial in Rome. The Senate is debating their doom.
The Senate gets divided into three groups. In the first and largest group, Pliny the younger convinces the other senators that there is no case for conviction. The death of Africius Dexter was a suicide, or very likely so, and the freedmen should be exempt from charge. The second group, slightly smaller, includes senators who are not willing to clear the freedmen from guilt. But they are not convinced enough to demand a harsh punishment. They opt for exiling the freedmen.
The smaller group, the third, is composed of senators who would have the freedmen all executed.
Most Senators expect Pliny the younger to count the votes on guilt, first, and then on punishment. The outcome in that case would be guilt, and the lesser punishment of exile, not death.
But Pliny refuses. He claims that coupling the options of exile and death and pitting them as a couple against acquittal is wrong. What do these punishments have in common, he asks? Surely, the distance between death and exile is larger than the distance between exile and acquittal. Pliny wants to count all three options as equal, and see what option would gain a simple majority. That is, which option has the larger pool of supporters.
This would mean, conveniently, that acquittal would win.
But that did not come to pass. The third group, the ones who want a death sentence, they “lie” and go over to the second group. Together, they have signed a majority for exiling the freedmen – much to the dismay of Pliny. As he moans in a letter to a friend, that was foul play.