My paper on the strong favorite betrayal criterion is available here. Feel free to comment on it in whatever the latest manuscript-related comment thread is.
Wednesday, August 25, 2010
Open thread for comments on manuscript
If you have something to say about my manuscript (linked at the top of the page), feel free to say it here.
When I initially commented here, I was just stripmining this paper for a formal definition of FBC. Now that I'm reading it more carefully, I like it more than I expected. Your results are surprisingly meaningful (and in accord with my practical experience), even though your formalism makes that meaning difficult to tease out.
A few specific comments so far, more to come.
Typo on page 16: you say N(xi) where you mean N(xy). One might almost think you were a native Spanish speaker (where y is named "greek i")
Figure 1 on page 20 would benefit from a dot and vector concretely showing the paradox. For instance, a 1>2>3 voter would be motivated to vote 2 in first place in order to prevent 3 from winning. I know that such a specific example would make the figure less generally-applicable, but by slicing the simplex you've already sacrificed generality, so I think that's OK.
OK, so I am looking at the problematic bit of section 7. So far, I don't understand why you start with a "three-way tie" and then perturb it. Wouldn't any point along the two-way tie surface between the C2 region and the cyclical region (where WLOG C3 is destined to win in the next stage) be enough to give you the paradox? If that is the case, then obviously you can't translate that whole surface outside the simplex without pushing one of the relevant regions out of the simplex; and if a region is out of the simplex, it is irrelevant, and the criteria defining it can be left out.
Obviously, this is still an intuitive argument, not formalized. But I'd like to see your response to see if I'm understanding you.
When I initially commented here, I was just stripmining this paper for a formal definition of FBC. Now that I'm reading it more carefully, I like it more than I expected. Your results are surprisingly meaningful (and in accord with my practical experience), even though your formalism makes that meaning difficult to tease out.
ReplyDeleteA few specific comments so far, more to come.
Typo on page 16: you say N(xi) where you mean N(xy). One might almost think you were a native Spanish speaker (where y is named "greek i")
Figure 1 on page 20 would benefit from a dot and vector concretely showing the paradox. For instance, a 1>2>3 voter would be motivated to vote 2 in first place in order to prevent 3 from winning. I know that such a specific example would make the figure less generally-applicable, but by slicing the simplex you've already sacrificed generality, so I think that's OK.
More to come later...
OK, so I am looking at the problematic bit of section 7. So far, I don't understand why you start with a "three-way tie" and then perturb it. Wouldn't any point along the two-way tie surface between the C2 region and the cyclical region (where WLOG C3 is destined to win in the next stage) be enough to give you the paradox? If that is the case, then obviously you can't translate that whole surface outside the simplex without pushing one of the relevant regions out of the simplex; and if a region is out of the simplex, it is irrelevant, and the criteria defining it can be left out.
ReplyDeleteObviously, this is still an intuitive argument, not formalized. But I'd like to see your response to see if I'm understanding you.