In particular it is impossible to have all of the below
If every voter prefers alternative X over alternative Y, then the group prefers X over Y.
If every voter’s preference between X and Y remains unchanged, then the group’s preference between X and Y will also remain unchanged (even if voters’ preferences between other pairs like X and Z, Y and Z, or Z and W change).
There is no “dictator”: no single voter possesses the power to always determine the group’s preference.
So it’s worthwhile to pick which bullet to bite first and design with that in mind as a limitation rather than just getting started and later on realize you’re boxed into a corner on this point.
So it’s worthwhile to pick which bullet to bite first and design with that in mind as a limitation rather than just getting started and later on realize you’re boxed into a corner on this point.
The easiest bullet to bite is the “ordinal preferences” bullet. If you allow the group to be indifferent between options, then the impossibility disappears. (You may end up with a group that uses a sensible voting rule that is indifferent between all options, but that’s because the group is balanced in its opposition.)
This doesn’t work so well if you want to use it as a decision rule. You may end up with some ranking which leaves you indifferent between the top two options, but then you still need to pick one. I think you need to explain why whatever process you use to do that wasn’t considered part of the voting system.
This doesn’t work so well if you want to use it as a decision rule. You may end up with some ranking which leaves you indifferent between the top two options, but then you still need to pick one. I think you need to explain why whatever process you use to do that wasn’t considered part of the voting system.
It seems to me that decision rules that permit indifference are more useful than decision rules that do not permit indifference, because fungibility of actions is a useful property. That is, I would view the decision rule as expressing preferences over classes of actions, but not specifying which of the actions to take within the class because it doesn’t see a difference between them. Considering Buridan’s Ass, it would rather “go eat hay” than “not go eat hay,” but doesn’t have a high-level preference for the left or right bale of hay, just like it doesn’t have a preference whether it starts walking with its right hoof or its left hoof.
Something must have a preference—perhaps the Ass is right-hoofed, and so it leads with its right hoof and goes to the right bale of hay—but treating that decision as its own problem of smaller scope seems superior to me than specifying every possible detail in the high-level decision problem.
If every voter’s preference between X and Y remains unchanged, then the group’s preference between X and Y will also remain unchanged (even if voters’ preferences between other pairs like X and Z, Y and Z, or Z and W change).
This is the condition I want to give up on. I’m not even convinced that it’s desirable.
Any parliamentary model will involve voting.
When voting arrows impossibly theorm is going to impose constraints that can’t be avoided http://en.m.wikipedia.org/wiki/Arrow’s_impossibility_theorem
In particular it is impossible to have all of the below
If every voter prefers alternative X over alternative Y, then the group prefers X over Y. If every voter’s preference between X and Y remains unchanged, then the group’s preference between X and Y will also remain unchanged (even if voters’ preferences between other pairs like X and Z, Y and Z, or Z and W change). There is no “dictator”: no single voter possesses the power to always determine the group’s preference.
So it’s worthwhile to pick which bullet to bite first and design with that in mind as a limitation rather than just getting started and later on realize you’re boxed into a corner on this point.
[will reformat when not typing on phone]
The easiest bullet to bite is the “ordinal preferences” bullet. If you allow the group to be indifferent between options, then the impossibility disappears. (You may end up with a group that uses a sensible voting rule that is indifferent between all options, but that’s because the group is balanced in its opposition.)
This doesn’t work so well if you want to use it as a decision rule. You may end up with some ranking which leaves you indifferent between the top two options, but then you still need to pick one. I think you need to explain why whatever process you use to do that wasn’t considered part of the voting system.
It seems to me that decision rules that permit indifference are more useful than decision rules that do not permit indifference, because fungibility of actions is a useful property. That is, I would view the decision rule as expressing preferences over classes of actions, but not specifying which of the actions to take within the class because it doesn’t see a difference between them. Considering Buridan’s Ass, it would rather “go eat hay” than “not go eat hay,” but doesn’t have a high-level preference for the left or right bale of hay, just like it doesn’t have a preference whether it starts walking with its right hoof or its left hoof.
Something must have a preference—perhaps the Ass is right-hoofed, and so it leads with its right hoof and goes to the right bale of hay—but treating that decision as its own problem of smaller scope seems superior to me than specifying every possible detail in the high-level decision problem.
This is the condition I want to give up on. I’m not even convinced that it’s desirable.
Something like independence of irrelevant alternatives or, at least, independence of clones is necessary to avoid spoiler effect, otherwise one can get situations like this one.
Yes I think independence of clones is quite strongly desirable.