Why is the majority not always right?
Why does majority voting fail to reveal the real preferences of society?
Look here. Suppose nine different United Russia and one Navalny are elected to the mayor. Suppose everyone has equal opportunity to promote themselves. Suppose each candidate has a policy of "all the assholes, and I am a smart one." Suppose that election campaigns of an equal budget led to an equal division of votes, and only a statistical error (1 vote) brought United Russia to mayor.
As a result, the selected mayor does not take into account the interests of 90% of the population.
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You will say that the second stage was invented for this. For the majority, this second stage makes it necessary to make a choice between two politicians whom they did not choose at the first stage.
(There is a curious problem on this score, I will put it at the end)
Here is a second example. There are three candidates, let's call them C, H, P. Let's simulate two situations: people vote by a majority (choose one) or people vote by the “order of preference” (for example, H> P> C means that H is better than P, and it's better than P than C). Will the election results be the same?
Take 60 voters.
Let the alignment be:
23 people voted C> N> P
19 people: P> N> S
16 people: N> P> C
2 persons: N> S> P
In comparison with the C P we have:
23 + 2 = 25 people because C is better than P; 19 + 16 = 35 people because P is better than C.
It can be said that the majority opinion is that P is better than C (35 is greater than 25, right?).
Comparing C and H, we will have:
23 people because C is better than H; 37 people for the fact that H is better than C.
From this we conclude that the majority prefers candidate H to candidate C.
Finally, compare H with P:
19 people for the fact that P is better than H; 41 people for being better than P.
It turns out that the majority is for H than for P.
Thus, by the will of the majority, it is expressed as: H> P; P> S; H> C, which can be combined into one attitude of preference N> P> C and, if it is necessary to choose one of the candidates, then candidate N. should be warned
At the same time, judging by the majority system, then you should choose C, because the majority voted for it (23 people).
This is called the Condorcet paradox and in many countries this situation is taken into account in voting systems.
Yes, about the puzzle.
In the country of Yurosii, where President Apten rules, the time of the new presidential election has approached. There are 100,000,000 voters in Yurosia, of which only one percent supports Apten. He wants to be democratically elected. “Democratic vote” Apten calls this: all voters are divided into several equal groups, then each of these groups is again divided into a number of equal groups, then these last groups are again divided into equal groups, and so on; in the smallest groups, elect a representative of the electoral group, then electors elect representatives to vote in an even larger group, and so on; Finally, representatives of the largest groups elect a president. Apten himself divides voters into groups. Suppose, with equal votes, the opposition wins. Can he organize elections in such a way that he is elected president?
The answer is later in the comments, if no one gets ahead of me.
Look here. Suppose nine different United Russia and one Navalny are elected to the mayor. Suppose everyone has equal opportunity to promote themselves. Suppose each candidate has a policy of "all the assholes, and I am a smart one." Suppose that election campaigns of an equal budget led to an equal division of votes, and only a statistical error (1 vote) brought United Russia to mayor.
As a result, the selected mayor does not take into account the interests of 90% of the population.
')
You will say that the second stage was invented for this. For the majority, this second stage makes it necessary to make a choice between two politicians whom they did not choose at the first stage.
(There is a curious problem on this score, I will put it at the end)
Here is a second example. There are three candidates, let's call them C, H, P. Let's simulate two situations: people vote by a majority (choose one) or people vote by the “order of preference” (for example, H> P> C means that H is better than P, and it's better than P than C). Will the election results be the same?
Take 60 voters.
Let the alignment be:
23 people voted C> N> P
19 people: P> N> S
16 people: N> P> C
2 persons: N> S> P
In comparison with the C P we have:
23 + 2 = 25 people because C is better than P; 19 + 16 = 35 people because P is better than C.
It can be said that the majority opinion is that P is better than C (35 is greater than 25, right?).
Comparing C and H, we will have:
23 people because C is better than H; 37 people for the fact that H is better than C.
From this we conclude that the majority prefers candidate H to candidate C.
Finally, compare H with P:
19 people for the fact that P is better than H; 41 people for being better than P.
It turns out that the majority is for H than for P.
Thus, by the will of the majority, it is expressed as: H> P; P> S; H> C, which can be combined into one attitude of preference N> P> C and, if it is necessary to choose one of the candidates, then candidate N. should be warned
At the same time, judging by the majority system, then you should choose C, because the majority voted for it (23 people).
This is called the Condorcet paradox and in many countries this situation is taken into account in voting systems.
Yes, about the puzzle.
In the country of Yurosii, where President Apten rules, the time of the new presidential election has approached. There are 100,000,000 voters in Yurosia, of which only one percent supports Apten. He wants to be democratically elected. “Democratic vote” Apten calls this: all voters are divided into several equal groups, then each of these groups is again divided into a number of equal groups, then these last groups are again divided into equal groups, and so on; in the smallest groups, elect a representative of the electoral group, then electors elect representatives to vote in an even larger group, and so on; Finally, representatives of the largest groups elect a president. Apten himself divides voters into groups. Suppose, with equal votes, the opposition wins. Can he organize elections in such a way that he is elected president?
The answer is later in the comments, if no one gets ahead of me.
Source: https://habr.com/ru/post/193018/
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