Ordinal Cheap Talk
Can comparative statements be credible even when absolute statements are not? For instance, can a professor credibly rank different students for a prospective employer even if she has an incentive to exaggerate the merits of each student? Or can an analyst credibly rank different stocks even if the client would be dubious about a recommendation to buy any one of them? We examine such problems in a multidimensional sender-receiver game where the sender has private information about multiple variables. We show that ordinal cheap talk, in which the variables are completely ordered by value or grouped into categories by value, can be credible even when interests are too opposed to support communication along any single dimension. Ordinal cheap talk is credible because it reveals both favorable and unfavorable information at the same time, thereby precluding any possibility of exaggeration. The communication gains from ordinal cheap talk can be substantial with only a couple of dimensions, and the payoffs from a complete ordering are asymptotically equivalent to full revelation as the number of variables becomes large. However, in various circumstances the sender can do better through a partial ordering that categorizes variables. Compared to other forms of cheap talk, ordinal cheap talk is exceedingly simple in that the sender only makes straightforward, comparative statements.
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