Imagine that a referendum had been held in the United States at the beginning of World War II in Europe to determine foreign policy toward Adolph Hitler. The issue might have been structured so that a policy would have been selected through a series of pairwise votes among three alternatives: declare war on Nazi Germany, support the Allies but do not get involved, or work toward friendly relations with the Nazis. Imagine that, after much public debate, all voters fall into one of three categories:

Hawks, who comprise 10 percent of voters fear that Hitler will take over Europe and harm the national security of the United States. Their preferred policy is to declare war; their second choice is to support the Allies.

Pragmatists, who make up 45 percent of the voters, want to discourage Hitler's plans to take over Europe and exterminate the Jews, but do not want to fight a war with the strong German army using U.S. troops. Their preferred policy, therefore is to support the allies; their second choice is to work toward friendly relations.

The Constitutionalists, representing 45 percent of the voters, prefer friendly relations. If aggressive action is to be taken against the Nazis, they prefer it to be through a declaration of war.

The table below summarizes the voters' policy choices under three different agendas.

Agenda A (Result: Peace)

Round 1 War vs. AlliesWar wins 55% to 45%
Round 2War vs. PeacePeace wins 90% to 10%

Agenda B (Result:Allies)

Round 1 War vs. PeacePeace wins 90% to 10%
Round 2Peace vs. AlliesAllies wins 55% to 45%

Agenda C (Result: War)

Round 1 Peace vs. AlliesAllies wins 55% to 45%
Round 2Allies vs. WarWar wins 55% to 45%
Agenda A offers declared war and support for the allies as the first alternatives. Next, it offers a choice between war and peace. Under agenda B, voters are offered choices between war vs. peace and peace vs. Allies. Agenda C offers peace vs. Allies and Allies vs. War. Despite the fact that no voting bloc changes its support, each agenda results in a different social choice!

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