4 ms·

> adding a 3rd candidate should not change the relative order of the first two This is, I think, the least justified requirement, since humans do naturally ref

> adding a 3rd candidate should not change the relative order of the first two This is, I think, the least justified requirement, since humans do naturally reframe situations when extra information is given, which can cause them to change their mind about previous decisions. To give a trivial example, suppose you were in a district which historically had a Democrat and a Republican candidate, and you always voted Democrat, but one year a far left independent candidate became popular and you feared they would attract most Democrat voters over to their camp. Given that scenario, it might make sense for you to vote for a moderate Republican instead. In any case, I think that the significance of Arrow's impossibility theorem is generally over-estimated (and it spreads as a meme because people like to think that all voting systems are bad so there's no reason to change the terrible one they have). For example, the theorem only applies to ordinal (ranked) voting systems, not cardinal (rated) ones, and only proves that the system cannot output "a community-wide (complete and transitive) ranking", so it is still possible to elect a small set of politicians who collectively embody the same preferences as the voters, and in direct proportion to them.

wtallis 5y ago
You've described an example where the addition of a third candidate causes a voter to strategically change who they're going to vote for, based on the expected outcomes under a particular voting system. That's not the same thing as the voter's actual preferences changing, it's just a manifestation of a limitation of a particular voting system.
- couchand 5y ago
  What exactly do you mean by "the voter's actual preferences"?
twic 5y ago
But all along, this person's preference is Democrat > Republican > Independent. That doesn't change. The fact that their best interests are served by casting a ballot which doesn't reflect that is exactly the problem!
- couchand 5y ago
  > their best interests are served by casting a ballot which doesn't reflect that is exactly the problem! You may be interested to hear about the Gibbard–Satterthwaite theorem then. Any non-dictatorial system with more than two alternatives is subject to tactical voting. Whoops!
  - dane-pgp 5y ago
    Unsurprisingly, I'm not a big fan of the Gibbard–Satterthwaite theorem either. It does apply more broadly than Arrow's, but my understanding is that even though a tactic will exist for every voting system, that tactic may require perfect information or at least isn't guaranteed to be actually exploitable by any voters taking part. If a tactic is so complicated and likely to backfire that no one ever attempts it (or the people that try it, on average, end up harming their cause) then I think that the threat of tactical voting is insignificant. What I don't know, unfortunately, is which voting system is best in terms of ease of voting honestly and difficulty of voting tactically. Determining that may involve knowing things like how people respond to polling data, or to one party telling their followers to fill out their ballots in a certain way, which might be hard to model.
- dane-pgp 5y ago
  > But all along, this person's preference is Democrat > Republican > Independent. That's a great point, thank you. I should have tried to describe a more subtle effect where someone sees the policies of the far left candidate and it taints their view of the Democrats, who they now view with suspicion, fearing the Democrats might secretly support the same extreme policies. Alternatively, a Republican voter might see the Overton window shift and consider the Democrats a more centrist party, and so drop their support for the Republicans. The problem is, these parties (and candidates) aren't spherical cows in a vacuum, and neither are voters. Voters have imperfect information and have to try to make predictions about which politicians are lying, and what direction the mood of the country is moving; so the addition of another party into an electoral contest can quite reasonably cause someone to change how they view the existing parties and even flip their support.

wtallis 5y ago

You've described an example where the addition of a third candidate causes a voter to strategically change who they're going to vote for, based on the expected outcomes under a particular voting system. That's not the same thing as the voter's actual preferences changing, it's just a manifestation of a limitation of a particular voting system.

couchand 5y ago
What exactly do you mean by "the voter's actual preferences"?

twic 5y ago

But all along, this person's preference is Democrat > Republican > Independent. That doesn't change. The fact that their best interests are served by casting a ballot which doesn't reflect that is exactly the problem!

couchand 5y ago
> their best interests are served by casting a ballot which doesn't reflect that is exactly the problem! You may be interested to hear about the Gibbard–Satterthwaite theorem then. Any non-dictatorial system with more than two alternatives is subject to tactical voting. Whoops!
- dane-pgp 5y ago
  Unsurprisingly, I'm not a big fan of the Gibbard–Satterthwaite theorem either. It does apply more broadly than Arrow's, but my understanding is that even though a tactic will exist for every voting system, that tactic may require perfect information or at least isn't guaranteed to be actually exploitable by any voters taking part. If a tactic is so complicated and likely to backfire that no one ever attempts it (or the people that try it, on average, end up harming their cause) then I think that the threat of tactical voting is insignificant. What I don't know, unfortunately, is which voting system is best in terms of ease of voting honestly and difficulty of voting tactically. Determining that may involve knowing things like how people respond to polling data, or to one party telling their followers to fill out their ballots in a certain way, which might be hard to model.
dane-pgp 5y ago
> But all along, this person's preference is Democrat > Republican > Independent. That's a great point, thank you. I should have tried to describe a more subtle effect where someone sees the policies of the far left candidate and it taints their view of the Democrats, who they now view with suspicion, fearing the Democrats might secretly support the same extreme policies. Alternatively, a Republican voter might see the Overton window shift and consider the Democrats a more centrist party, and so drop their support for the Republicans. The problem is, these parties (and candidates) aren't spherical cows in a vacuum, and neither are voters. Voters have imperfect information and have to try to make predictions about which politicians are lying, and what direction the mood of the country is moving; so the addition of another party into an electoral contest can quite reasonably cause someone to change how they view the existing parties and even flip their support.