How Math Explains the World.pdf
There are many different ways of showing this fact (in fact, when I give exams in a first-year course in topology, I ask studen ...
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Section IV The Unattainable Utopia ...
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12 Cracks in the Foundation The Foundation of Democracy Elections are the foundation of democracy. We vote on matters as impor- ...
in case no candidate has an electoral majority, but the 1824 election re- vealed that the system had not been fixed. The leading ...
states in an electoral college of 100 votes. The states have 49, 48, and 3 electoral votes. To compute the BPI of the 3-vote sta ...
method to use in a democracy goes back more than two centuries. Probably the first person to notice that there were problems ass ...
dead in his cell. It is not known whether he died of natural causes or was killed. Condorcet’s present fame rests neither on his ...
This simple example illustrates a problem that would perplex social sci- entists for more than a century: How can one translate ...
ballots, which are then reexamined. The whole process is repeated, until only two remain. The winner of this two-person contest ...
Admittedly, the above tabulation does seem to resemble something you see when you visit your optometrist, but let’s check the re ...
Number of Ballots First Choice Second Choice 18 A C 12 C A 10 C A 9 C A 4 C A 2 C A So C survives by a vote of 37 to 18. Numeri ...
of this hypothetical election, and is asked whether he can come up with something better. After studying the example, he might o ...
encountered by existing methods, but after each proposed algorithm eliminated one problem but introduced another, he began to co ...
loser simply results in his or her being removed from the ballot. Sup- pose we have an election with the following collection of ...
the Nobel Prize in Economic Science in 1972, was that no transitive vot- ing method can satisfy all three of the above condition ...
near unanimity is not an uncommon occurrence in dictatorships. In pre- war Iraq, Saddam Hussein’s choices were reported to have ...
important elections in the United States simply require the voter to make a single selection, so in practice the Arrow’s theorem ...
mathematics) in areas vastly different from the social preference setting for which it was originally formulated. I can’t resist ...
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