>Condorcet formalized the idea that group preferences are also non-transitive. If people prefer Hanselman to me. And they prefer me to Guthrie. It does not necessarily mean they will prefer Hanselman to Guthrie. It could be that Guthrie would pull a surprise upset when faced head to head with Hanselman.
I found this by far the most interesting assertion, but the examples under "Historical Examples" don't demonstrate this phenomenon at all.
For instance, the author asserts that the Nader spoiler effect demonstrates nontransitive preference relationships. But from my reading, it wasn't the case that that group as a whole preferred (Gore over Nader) and (Nader over Bush) but (Bush over Gore). It was simply that due to the structure of the election, they happened to elect Bush. While this ties into the author's point about the "unfairness" of elections, it doesn't demonstrate nontransitive relationships in group preferences.
Could someone post an example of a group preference configuration in which the group prefers (A over B) and (B over C) but (C over A)?
I understand the concept of nontransitive relationships in general, but in the specific domain of fitness for office, I can't work out how this would come to be.
It's late and I'm tired but I think in the following situation -
49% vote Bush, 42% vote Gore, 9% vote Nader.
All Bush voters prefer Nader over Gore (unlikely!). All Nader voters prefer Gore over Bush. Half of Gore voters prefer Bush over Nader.
- If the election was Gore:Bush, Gore would win 51:49
- If the election was Bush:Nader, Bush would win 70:30
- If the election was Gore:Nader, Nader would win 42:58
The group prefers Gore over Bush (A over B) and Bush over Nader (B over C) but Nader over Gore (C over A).
I am wondering that too. He also gave the example of Ford beating Reagan (in the Republican primary), Carter beating Ford in the general election in 1976, and then Reagan beating Carter in 1980, but this is also not a great example since the Republican primary group is very different than the general electorate.
>Condorcet formalized the idea that group preferences are also non-transitive. If people prefer Hanselman to me. And they prefer me to Guthrie. It does not necessarily mean they will prefer Hanselman to Guthrie. It could be that Guthrie would pull a surprise upset when faced head to head with Hanselman.
I found this by far the most interesting assertion, but the examples under "Historical Examples" don't demonstrate this phenomenon at all.
For instance, the author asserts that the Nader spoiler effect demonstrates nontransitive preference relationships. But from my reading, it wasn't the case that that group as a whole preferred (Gore over Nader) and (Nader over Bush) but (Bush over Gore). It was simply that due to the structure of the election, they happened to elect Bush. While this ties into the author's point about the "unfairness" of elections, it doesn't demonstrate nontransitive relationships in group preferences.
Could someone post an example of a group preference configuration in which the group prefers (A over B) and (B over C) but (C over A)?
I understand the concept of nontransitive relationships in general, but in the specific domain of fitness for office, I can't work out how this would come to be.