Haven't read either yet, but FYI there is a reply to Barnett's voting paper. Enoch and Liron, THE CASE FOR VOTING TO CHANGE THE OUTCOMES IS WEAKER THAN IT MAY SEEM
Haven't read either yet, but FYI there is a reply to Barnett's voting paper. Enoch and Liron, THE CASE FOR VOTING TO CHANGE THE OUTCOMES IS WEAKER THAN IT MAY SEEM
Richard is right that the criticism of the binomial model is entirely separate from the lower bound I defend. But I should make a comment about their reply.
(This might not make much sense if you haven't read the papers yet, but oh well.)
In arguing for the lower bound, I don't claim that unimodality is true always and everywhere. Liron and Enoch are right that, in principle, there can be exceptions. (Interestingly, the only actual empirical "exception" they foundтАФsee the appendix of their paperтАФwas from a forecast about how many *senate seats* the republicans would win, rather than a forecast about what share of the vote a given candidate would earn. That's about something different. But nonetheless, I grant that there can be exceptions.)
What I do claim is that (1) unimodality is **often** true and that (2)when unimodality is true, it can be used to place a lower bound on the probability of casting a decisive vote.
Just glance at the graph at the top of the page, or any of the graphs further down. They're all unimodal. Here's a quote from the primer: "all outcomes within the margin of error are not equally likely; instead, those closer to the mean of the distribution are more probable."
In the paper, I also give reasons for thinking that unimodality will often be true. Say you're trying to estimate how many red and blue M&Ms there are in an enormous, shaken bag of millions of M&Ms. You do a sample and find that 55% are red. Roughly (setting aside your prior probability over the different proportions), that finding is likeliest if the true proportion of red to blue is 55/45. It's less likely if the true proportion is 50/50. And it's extremely unlikely if the true proportion is 99/1.
I don't think Liron and Enoch necessarily take issue with any of this. They even say: "We donтАЩt claim here to offer a comprehensive survey of the literature, nor do we attempt here an assessment of how often it is that Partial Unimodality fails. Instead, our purpose here is to show that such failures are sometimes in place, and indeed,knowably so."
Yes, probably worth assigning both! A key upshot from the reply: "while Barnett is correct to assert that BrennanтАЩs assumption of voter independence is unrealistic, our criticism of BarnettтАЩs use of Partial UnimodalityтАФsomewhat ironicallyтАФshows that Barnett, too, falls prey to a rather similar (if less acute and conclusive) flaw."
Haven't read either yet, but FYI there is a reply to Barnett's voting paper. Enoch and Liron, THE CASE FOR VOTING TO CHANGE THE OUTCOMES IS WEAKER THAN IT MAY SEEM
A Reply to Zach Barnett
Richard is right that the criticism of the binomial model is entirely separate from the lower bound I defend. But I should make a comment about their reply.
(This might not make much sense if you haven't read the papers yet, but oh well.)
In arguing for the lower bound, I don't claim that unimodality is true always and everywhere. Liron and Enoch are right that, in principle, there can be exceptions. (Interestingly, the only actual empirical "exception" they foundтАФsee the appendix of their paperтАФwas from a forecast about how many *senate seats* the republicans would win, rather than a forecast about what share of the vote a given candidate would earn. That's about something different. But nonetheless, I grant that there can be exceptions.)
What I do claim is that (1) unimodality is **often** true and that (2)when unimodality is true, it can be used to place a lower bound on the probability of casting a decisive vote.
In defense of (1), here is a primer how election forecasts work from 538: <https://fivethirtyeight.com/features/how-the-fivethirtyeight-senate-forecast-model-works/>
Just glance at the graph at the top of the page, or any of the graphs further down. They're all unimodal. Here's a quote from the primer: "all outcomes within the margin of error are not equally likely; instead, those closer to the mean of the distribution are more probable."
In the paper, I also give reasons for thinking that unimodality will often be true. Say you're trying to estimate how many red and blue M&Ms there are in an enormous, shaken bag of millions of M&Ms. You do a sample and find that 55% are red. Roughly (setting aside your prior probability over the different proportions), that finding is likeliest if the true proportion of red to blue is 55/45. It's less likely if the true proportion is 50/50. And it's extremely unlikely if the true proportion is 99/1.
I don't think Liron and Enoch necessarily take issue with any of this. They even say: "We donтАЩt claim here to offer a comprehensive survey of the literature, nor do we attempt here an assessment of how often it is that Partial Unimodality fails. Instead, our purpose here is to show that such failures are sometimes in place, and indeed,knowably so."
tl;dr: I'm saying "Often P." They're saying "Sometimes ~P!"
Yes, probably worth assigning both! A key upshot from the reply: "while Barnett is correct to assert that BrennanтАЩs assumption of voter independence is unrealistic, our criticism of BarnettтАЩs use of Partial UnimodalityтАФsomewhat ironicallyтАФshows that Barnett, too, falls prey to a rather similar (if less acute and conclusive) flaw."