Smith Set Comparison
The Schwartz set is closely related to and is always a subset of the Smith set. The Smith set is larger if and only if a candidate in the Schwartz set has a pairwise tie with a candidate that is not in the Schwartz set. For example, given:
- 3 voters preferring candidate A to B to C
- 1 voter preferring candidate B to C to A
- 1 voter preferring candidate C to A to B
- 1 voter preferring candidate C to B to A
then we have A pairwise beating B, B pairwise beating C, and A tying with C in their pairwise comparison, making A the only member of the Schwartz set, while the Smith set on the other hand consists of all the candidates.
Read more about this topic: Schwartz Set
Famous quotes containing the words smith, set and/or comparison:
“Every individual necessarily labours to render the annual revenue of the society as great as he can. He generally, indeed, neither intends to promote the publick interest, nor knows how much he is promoting it.... He intends only his own gain, and he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention.”
—Adam Smith (1723–1790)
“You should try to understand every thing you see and hear; to act and judge for yourselves; to remember you each have a soul of your own to account for; M a mind of your own to improve. When you once get these ideas fixed, and learn to act upon them, no man or set of men, no laws, customs, or combinations of them can seriously oppress you.”
—Jane Grey Swisshelm (1815–1884)
“Clay answered the petition by declaring that while he looked on the institution of slavery as an evil, it was ‘nothing in comparison with the far greater evil which would inevitably flow from a sudden and indiscriminate emancipation.’”
—State of Indiana, U.S. public relief program (1935-1943)