This paper analyzes simple models of editorial control. Starting from the framework developed by Krishna and Morgan (2001a), we analyze two-sender models of cheap talk where one or more of the senders has the power to veto messages before they reach the receiver. A characterization of the most informative equilibria of such models is given. It is shown that editorial control never aids communication and that for small biases in the senders’ preferences relative to those of the receiver, necessary and sufficient conditions for information transmission to be adversely affected are (i) that the senders have opposed preferences relative to the receiver and (ii) that both senders have powers of editorial control. It is shown that the addition of further senders beyond two weakly decreases information transmission when senders exercising editorial control are anonymous, and weakly increases information transmission when senders exercising editorial control are observed.
This paper has its genesis in a chapter of my PhD completed at the University of Cambridge. I thank Robert Evans for his kind advice, as well as the editor and two anonymous referees. The author is the recipient of a Discovery Early Career Researcher Award funded by the Australian Research Council.
: only sender 2 can block, opposed biases
In Period 2, S2 decides to “block” or “allow” S1’s message.
Strategies for S1 and S2 are:
. For example, a strategy could be to inform R of the correct state or to inform R whether is below or above .
. For example, a strategy could be to inform R of the correct state and never block, or to block when it indicates the state is below a certain threshold and otherwise give no further information.
Fully revealing equilibrium
Let , when , when . Let:
If R observes consistent with these equilibrium strategies then . If R observes which are inconsistent with these equilibrium strategies then when , when . Hence S2 is believed only when it would not be profitable to him for R to believe his message when S1’s message correctly indicates . Set:
: both senders can block own message, opposed biases
In Period 2 S1 and S2 decides to “block” or “allow” their own messages.
Strategies for S1 and S2 are:
Fully revealing equilibrium
Let , when , when . For all , let:
If R observes consistent with these equilibrium strategies then . If R observes which are inconsistent with these equilibrium strategies then when and/or . Otherwise, let . Hence S2 is believed only when it would not be profitable to him for R to believe his message when S1’s message correctly indicates . Set:
Note that for given , the lowest y that could be induced by S2 is , so S2 can never incentivize S1 to play .
: both senders can block all messages, blocker observed, opposed biases
Strategies for S1 and S2 are as in .
Equilibrium with blocking area of size
Let , when . Let , when . Let , when . If R observes consistent with these equilibrium strategies then . If R observes which are inconsistent with these equilibrium strategies and then let . If and either
then . Otherwise, let . Beliefs when blocking occurs are
Let be determined by these beliefs. Let
Note the strict inequality above and that in this equilibrium both S1 and S2 play when .
Fully revealing equilibrium with players
Let be such that if , for a majority of , then . If and no message is sent by a majority of senders, let . If , then let . If , then let . For other blocking possibilities, let . Let be determined by these beliefs.
For all , for , let . Let
We construct a non-monotonic equilibrium when . We divide the available messages of into two sets of messages so there are in effect only two messages available to the senders. R’s beliefs are as follows:
Equilibrium strategies for the senders are then as follows:
Farrell, J., and R.Gibbons. 1989. “Cheap Talk with Two Audiences .” AER 79:1212–23.Search in Google Scholar
Krishna and Morgan (2001b) also study the case where the two senders send messages sequentially rather than simultaneously. In such a model, it is impossible to achieve full revelation of private information. As the goal of the paper is to present the simplest model of editorial control, the author chooses to present results stemming from the simultaneous senders model.
Although both experts have the same information, the sender with editorial control can still gain from employing a further sender when payoffs are compared to equilibrium payoffs of the one sender game.
Such a situation is by no means unusual. Research for policy formation bodies – “think tanks” – is often undertaken by people who are by no means experts in any sense of the word. The entire weight attributed to their opinions comes from the fact that they are operating under the aegis of a well-known organization. Were they to leave the organization and write some research on their own it is unlikely that many people would read it or that any press coverage would be achieved.
For example, in every UK general election since 1992, at least 28% of readers of the most read newspaper in the United Kingdom, the Sun, have voted for the largest party opposed to the party supported by the newspaper. The Sun supported the Conservatives in 1992, 2010; Labor in 1997, 2001, 2005. Source: http://www.ipsos-mori.com/researchpublications/researcharchive/2476/Voting-by-Newspaper-Readership-19922010.aspx.
As of January 7th 2012, English Wikipedia contained 3,840,444 articles. During 2011 there were 59 requests to open arbitration cases, only 13 of which were accepted. 16 cases were heard and settled by the arbitration committee in 2011. See: http://en.wikipedia.org/wiki/Wikipedia:Requests for arbitration/Statistics 2011
In the context of Wikipedia, such a reduction in anonymity is provided by the availability of the IP addresses of those who make changes to articles. This information can be used to identify possible editing by interested parties, such as edits of the biographical information of US congressmen via congressional IP addresses. See: http://en.wikipedia.org/wiki/U.S. Congressional staff edits to Wikipedia.
For example, if there existed a message “black” that a sender sent in equilibrium when the state was “white” then the “meaning” of “black” would be “white”.
Non-monotonic equilibria do exist. An example is given in Appendix B.
We note that criticisms of Krishna and Morgan (2001a) also apply to the current paper. In particular, the equilibrium constructions rely on the perfect observation of the by the senders (Battaglini 2002). It is plausible to think that disagreement between senders over the state of the world could be a reason for message blocking. The current paper abstracts from such possibilities to focus on strategic considerations.
This is similar to the observation of Dessein (2002) that R may want to commit to playing the best action for the sender (allow the sender to choose the action) to induce full revelation.
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