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Robert Israel
Robert Israel
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For the case of $3$ random variables, choose two of them (at random) and compare the sample means of the first half of the samples. Then compare the sample means of the second half of the samples for the winner of the first round and the third random variable. You'll have probability greater than $1/3$ of the result being correct. The random choice of the initial pair to compare is, of course, necessary for this.

Similarly, with $n$ random variables, conduct a "knockout tournament" such that at each level a different set of samples is used to(so that you maintain independence of the pairwise comparisons).

For the case of $3$ random variables, choose two of them (at random) and compare the sample means of the first half of the samples. Then compare the sample means of the second half of the samples for the winner of the first round and the third random variable. You'll have probability greater than $1/3$ of the result being correct. The random choice of the initial pair to compare is, of course, necessary for this.

Similarly, with $n$ random variables, conduct a "knockout tournament" such that at each level a different set of samples is used to maintain independence.

For the case of $3$ random variables, choose two of them (at random) and compare the sample means of the first half of the samples. Then compare the sample means of the second half of the samples for the winner of the first round and the third random variable. You'll have probability greater than $1/3$ of the result being correct. The random choice of the initial pair to compare is, of course, necessary for this.

Similarly, with $n$ random variables, conduct a "knockout tournament" such that at each level a different set of samples is used (so that you maintain independence of the pairwise comparisons).

Source Link
Robert Israel
Robert Israel
  • 54.2k
  • 1
  • 76
  • 152

For the case of $3$ random variables, choose two of them (at random) and compare the sample means of the first half of the samples. Then compare the sample means of the second half of the samples for the winner of the first round and the third random variable. You'll have probability greater than $1/3$ of the result being correct. The random choice of the initial pair to compare is, of course, necessary for this.

Similarly, with $n$ random variables, conduct a "knockout tournament" such that at each level a different set of samples is used to maintain independence.