Post History
#2: Post edited
by
r~~
·
2023-09-27T23:51:07Z (8 months ago)
- > with randomized positions in the chart
Implicit in this description of your model is the notion that every location for a separator line is equally likely. This is false; lines are much less likely to appear near other lines than farther away. This is because to have two lines very close to each other, some candidate would have had to have received only a handful of votes; if each voter votes randomly, this is much less likely than a distribution where all candidates have roughly equal votes.- The actual probability that one candidate obtains a majority of votes, for $n > 2$ candidates, depends on the size of your voting population and approaches zero as the population grows, so your other formula isn't correct either. (The number of votes a single candidate receives is a random variable with a binomial distribution, and the standard deviation of a binomial distribution is proportional to the square root of the number of voters, which grows more slowly than the number of votes needed for a majority.)
- > with randomized positions in the chart
- Implicit in this description of your model is the notion that every location for a separator line is equally likely. This doesn't describe the actual distribution of vote totals; with random voters, lines are much less likely to appear near other lines than farther away. This is because to have two lines very close to each other, some candidate would have had to have received only a handful of votes; if each voter votes randomly, this is much less likely than a distribution where all candidates have roughly equal votes.
- The actual probability that one candidate obtains a majority of votes, for $n > 2$ candidates, depends on the size of your voting population and approaches zero as the population grows, so your other formula isn't correct either. (The number of votes a single candidate receives is a random variable with a binomial distribution, and the standard deviation of a binomial distribution is proportional to the square root of the number of voters, which grows more slowly than the number of votes needed for a majority.)
#1: Initial revision
by
r~~
·
2023-09-27T23:50:06Z (8 months ago)
> with randomized positions in the chart Implicit in this description of your model is the notion that every location for a separator line is equally likely. This is false; lines are much less likely to appear near other lines than farther away. This is because to have two lines very close to each other, some candidate would have had to have received only a handful of votes; if each voter votes randomly, this is much less likely than a distribution where all candidates have roughly equal votes. The actual probability that one candidate obtains a majority of votes, for $n > 2$ candidates, depends on the size of your voting population and approaches zero as the population grows, so your other formula isn't correct either. (The number of votes a single candidate receives is a random variable with a binomial distribution, and the standard deviation of a binomial distribution is proportional to the square root of the number of voters, which grows more slowly than the number of votes needed for a majority.)