# math

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## Elections and Strategic Voting | Video Lectures

Institute for Advanced Study U.S. presidential elections often drive many citizens to vote strategically—to vote for a candidate they do not like in hope of preventing someone they dislike even more from winning. Many who favored Ralph Nader in the 2000 election ended up voting for Al Gore (though not enough to stop George W.
The Stanley Reiter diagram above illustrates a game of mechanism design. The upper-left space depicts the type space and the upper-right space X the space of outcomes.

## What is Mechanism Design?

Two children are squabbling over how to divide a pie. We need a method to divide the pie fairly. Parents will already know one answer—one child cuts and the second child chooses.

## Nirvana fallacy

The nirvana fallacy is the informal fallacy of comparing actual things with unrealistic, idealized alternatives. It can also refer to the tendency to assume that there is a perfect solution to a particular problem. A closely related concept is the perfect solution fallacy . By creating a false dichotomy that presents one option which is obviously advantageous—while at the same time being completely implausible—a person using the nirvana fallacy can attack any opposing idea because it is imperfect. The choice is not between real world solutions and utopia ; it is, rather, a choice between one realistic possibility and another which is merely better . [ edit ] History
The economic calculation problem is a criticism of using economic planning as a substitute for market-based allocation of the factors of production . It was first proposed by Ludwig von Mises in his article Economic Calculation in the Socialist Commonwealth and later expanded upon by Friedrich Hayek . [ 1 ] [ 2 ] In his first article, Mises describes the nature of the price system under capitalism and describes how individual subjective values are translated from qualitative or metaphysical data into the cardinal objective information necessary for rational allocation of resources in a catallactic environment . In market exchanges, prices convey embedded information about the abundance of resources as well as their desirability , which in turn allows corrections that prevent shortages and surpluses .

## Economic calculation problem

In mechanism design , a process is incentive-compatible if all of the participants fare best when they truthfully reveal any private information asked for by the mechanism. As an illustration, voting systems which create incentives to vote dishonestly lack the property of incentive compatibility. In the absence of dummy bidders or collusion , a second price auction is an example of a mechanism that is incentive compatible. There are different degrees of incentive-compatibility: in some games , truth-telling can be a dominant strategy .

## Tactical voting

In voting systems , tactical voting (or strategic voting or sophisticated voting or insincere voting ) occurs, in elections with more than two candidates, when a voter supports a candidate other than his or her sincere preference in order to prevent an undesirable outcome. [ 1 ] It has been shown by the Gibbard–Satterthwaite theorem that, if a voting method for choosing one of several options is completely strategy-free, then it must be either dictatorial or nondeterministic (that is, might not select the same outcome every time it is applied to the same set of voter preferences). For instance, the random ballot voting method, which randomly selects the ballot of a single voter and uses this to determine the outcome, is strategy-free, but may result in different choices being selected if applied multiple times to the same set of ballots.
Stuff happens. The weather forecast says it’s sunny, but you just got drenched. You got a flu shot—but you’re sick in bed with the flu. Your best friend from Boston met your other best friend from San Francisco. Coincidentally.