An Experimental Study of Strategic Voting and Accuracy of Verdicts with Sequential and Simultaneous Voting

Round 1

Reviewer 1 Report

See attached file

Comments for author File: Comments.pdf

Author Response

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Reviewer 2 Report

This paper makes a straightforward contribution: a lab test of voting behaviour in Condorcet Jury settings. In particular, it focuses on specific setup and compares a qualified majority voting rule with unanimity with both simultaneous and sequential voting. The main takeaway is that wh8ile we observe substantial strategic voting (as already documented in slightly different setups), outcomes under unanimity are quite different from what the strategic voting literature would predict. Furthermore, sequential voting behavior is very different from simultaneous voting behavior, with suggestive evidence that many subjects learn about the state from others' votes.

I have found the paper mostly well written and clear. However, I believe it would benefit from a revision that would take into account some issues I highlight here.

 

1. The information cascade part of the paper is probably the most interesting and new. However, it currently fails to provide a test of a theory. It would be interesting if the author could devise such a test.
2. In general, is the paper well-motivated. I found the title very uninformative about what the paper is about and the introduction focuses a lot on some properties of unanimity, but not on others the experiment may tell us things about (see below). Maybe a bit of rewriting of the introduction and a more informative title would help here.
3. Linked to comment 1, I notice at the end of page 11 that voting behavior is not consistent with the cascade model sugegsted by the authors. In fact, voters heavily "discount" others' votes--i.e., they do not behave as if others voted sincerely/informatively, but rather as if others may have voted strategically and their vote is not necessarily the signal. This should be discussed--and potentially could be a very interesting part of the paper.
4. The description of the experiment is a bit sloppy. The qualified majority rule is not described very clearly, but only at some point it appears suddenly as "under the 5/6 majority rule used." Also, O have found the phrasing "at a US university" a bit weird... why not saying which one?
5. Table 1 presents conditional probabilities. It should be clarified. In general, there are way too many things that are left to the reader to understand, especially about the tables.
6. P. 7 says "in contrast, the timing of votes...". The contrast would be more clear if we had p-values also for this test in the table.
7. P. 8, parenthesis in the middle of the page, "thinking that their payoff will determine...". You mean "their vote"?
8. The explanation on p.8-9 is quite long. I am pretty sure it could be explained better, perhaps no need for a numerical example.
9. Table 6 presents numbers of occurrences, hut conditional probabilities would be more clear, I believe.
10. A thing never discussed clearly, but that is quote striking to me, is that there are no convictions at all with unanimity. The paper focuses on wrong convictions, but the main empirical result seems to be that simply it's impossible to convict anybody if we require unanimous voting. Why? Shouldn't the paper discuss this and provide some insights?

Author Response

We have written all of the responses to the reviewers in one file.

Author Response File: Author Response.docx

Reviewer 3 Report

The manuscript under consideration presents a decontextualised Condorcet jury experiment in both sequential and simultaneous voting under either a majority or unanimity rule. Well-established theoretical results state that jurors, who receive private signals about the likely state of the world, should condition their expectation on their vote being pivotal, rather than revealing this private information through their vote. This creates a paradox in which unanimity rules may lead to higher conviction rates. In contrast to this theoretical prediction, the typical experimental result is that jurors vote more with their signal than is predicted however.

Based on the results of this experiment, it seems that jurors are more likely to condition their vote on others' information in the sequential setup than in the simultaneous voting setup. This makes sense, as in the sequential setup jurors are actually put in the information state which is only a hypothetical or counterfactual in the simultaneous setup. 

The experiment is designed well and the results support the authors' conclusions. I would nevertheless recommend some changes to the writing before this article may be published. 

Firstly, the authors need to make clearer from the beginning what their specific contribution to the literature is -- something which I still don't have a great sense of. Is this the first experiment to contrast sequential/simultaneous and majority/unanimity rules? Is the contribution that this is done under asymmetric incentives? (wrongly convicting is costlier than a wrong acquittal). This should be in the introduction, if not the abstract.

Next, I think much more needs to be said about the relationship between the swing voter's curse and the winner's curse, only addressed presently at the end. This is the reason why we expect sequential and simultaneous voting to be different even when theory says they should be the same. So this failure to incorporate information from the counterfactual of being pivotal motivates the entire paper, and a narrative should be built around this.

Finally, I don't think sequential voting speaks to the issue of deliberation. Jurors don't just say how they are going to vote, they usually need to justify their decision to others, i.e. reveal their private information. An environment where only voting reveals information is not a model of deliberation. 

 

Author Response

We have written all of the responses to the reviewers in one file.

Author Response File: Author Response.docx

Reviewer 4 Report

This manuscript presents the results of an experiment in which participants in groups of 12 vote on whether to convict or acquit a defendant. The authors use a 2x2 design that varies whether (a) the decision is made through anonymity or a 5/6^th majority and (b) whether group members vote simultaneously or sequentially. The main result is that participants are more likely to follow Nash equilibrium predictions in the sequential case. The authors also look at group decisions and information cascades, finding significant evidence that the latter take place.

Overall, this is a great paper that would be a perfect fit for this journal. It is already extremely well-written and is extremely comprehensive in both its review of the literature and its analysis. My suggestions therefore relate only to a few minor changes that the authors may wish to incorporate in subsequent versions (but should also be free to discard).

First, it would be nice if the authors could include the instructions not just for the sequential anonymity treatment, but also for the other three treatments.

Second, when referring to the Dekel and Piccone (2000) results, the authors mention that the “simultaneous” equilibrium is “an” equilibrium for the sequential game. Are there other equilibria in the sequential game too? If so, it would be worth at least briefly discussing the nature of these equilibria, and whether behavior in the experiment may be consistent with them.

Third, I was a little confused when the authors first introduced the “5/6” majority rule. Perhaps it would be useful to state explicitly that this refers to a “5/6^th majority” (instead of simple majority), or write “5/6^th” instead of “5/6” (on page 6).

Fourth, I wonder whether in the analysis in Table 5 (and similar tables), the “number of guilty votes” variable could also capture the “number of any votes” cast previously, as would be the case if voters systematically vote differently towards the end of a round anyway. It could perhaps be good to show that including a “number of previous votes” variable in this table does not change the results.

Author Response

We have written all of the responses to the reviewers in one file.

Author Response File: Author Response.docx