Organizing Contests for Status: The Matthew Effect versus the Mark Effect

Transcription

1 Organizing Contests for Status: The Matthew Effect versus the Mark Effect Edward Bishop Smith Matthew S. Bothner University of Chicago Joel M. Podolny Yale University May 17, 2008

2 What is the best way to design tournaments for status, where individuals, such as scientists (Merton 1968) or technologists (Kanter et al 1997), labor in part for the esteem of their peers?

3 ?

4 ??

5 ?? Allocation of Resources Two competing views cumulative advantage and redistribution

6 "For unto every one that hath shall be given, and he shall have abundance: but from him that hath not shall be taken away even that which he hath. - Matthew 25:29 Merton (1968); the near monopolization of prestige by a few or a single luminary--a natural consequence of the Matthew Effect--benefits the entire system by ratcheting up incumbents levels of engagement. Lazear and Rosen (1988); higher wage differentials lead to higher effort, thus improving individual and aggregate return. The rich get richer the poor get poorer. Matthew Effect! Allocation of Resources

7 But many who are first will be last, and the last will be first. - Mark 10:31 McAdam (1982), Walker and Smith (2001); consequences of relative deprivation and negative reactions to aggregate levels of inequality. Akerlof and Yelen (1990); wage differentials undermine cooperation and reduce effort, resulting in diminished overall return. Forced subsidization of the status-poor by the status-rich. Mark Effect! Allocation of Resources

8 Design rules of the formal model Start with a system of n actors who begin as status equals and progressively come to inhabit distinct positions in an emergent status hierarchy. 5 S it!," ( ) ( ) =!+"S jt # D ijt j A B C D E ID Centrality Bonacich Centrality A B C D E

9 Design rules of the model Start with a system of n actors who begin as status equals and progressively come to inhabit distinct positions in an emergent status hierarchy. S it!," ( ) ( ) =!+"S jt # D ijt Initial between-actor differences are limited to variations in levels of ability, A. Ability is defined a prior and remains constant. In each round, actors choose to produce at a level of quality that is commensurate with both their ability and their individual cost of production. j S F,it +1, Q * it ;!S F,it +1 ( Q ) it /!Q it =!C ( F,it Q ) it /!Q it C F,it ( Q ) it = kq a it A!b!c i S it

10 Design rules of the model Start with a system of n actors who begin as status equals and progressively come to inhabit distinct positions in an emergent status hierarchy. S it!," ( ) ( ) =!+"s jt # D ijt Initial between-actor differences are limited to variations in levels of ability, A. Ability is defined a prior and remains constant. In each round, actors choose to produce at a level of quality that is commensurate with both their ability and their individual cost of production. j S F,it +1, Q * it ;!S F,it +1 ( Q ) it /!Q it =!C ( F,it Q ) it /!Q it C F,it ( Q ) it = kq a it A!b!c i S it As a result of production quality, actors receive varying levels of deference from one another that equate to transfers of status.

11 Design rules of the model Start with a system of n actors who begin as status equals and progressively come to inhabit distinct positions in an emergent status hierarchy. S it!," ( ) ( ) =!+"s jt # D ijt Initial between-actor differences are limited to variations in levels of ability, A. Ability is defined a prior and remains constant. In each round, actors choose to produce at a level of quality that is commensurate with both their ability and their individual cost of production. j S F,it +1, Q * it ;!S F,it +1 ( Q ) it /!Q it =!C ( F,it Q ) it /!Q it C F,it ( Q ) it = kq a it A!b!c i S it As a result of production quality, actors receive varying levels of deference from one another that equate to transfers of status. c > 0; Matthew Effect c < 0; Mark Effect

12 Individual-Level Profit / Social Welfare c > 0 : Matthew Effect. Fanning out processes. Rewarding statusrich results in the failure of the lowest status actor (status 0). The result is that this otherwise capable actor is rendered ineffectual as a producer.! it +1 = S it +1 " C it c < 0 : Mark Effect. The elite subsidizes the non-elite in order to buffer the system from nonproduction by the non-elite (but able). Note the difference In the profit level of the elite here compared to the chart above.

13 Profit Individual-Level Profit / Social Welfare c > 0 : Matthew Effect. Fanning out processes. Rewarding statusrich results in the failure of the lowest status actor (status 0). The result is that this otherwise capable actor is rendered ineffectual as a producer time! it +1 = S it +1 " C it Profit c < 0 : Mark Effect. The elite subsidizes the non-elite in order to buffer the system from nonproduction by the non-elite (but able). Note the difference In the profit level of the elite here compared to the chart above time

14 Profit time System-Level Profit / Aggregate Social Welfare c > 0 : Matthew Effect. Resources are pushed in the direction of the status elites. (Elites face less costs of production as a function of their status).! t +1 = # S it +1 " C it n Profit c < 0 : Mark Effect. Resources are pushed in the direction of the status non-elites. (Non-elites face less costs) time

15 High and Low status (Open and Closed) systems Thus far I have treated the model as reflective of status contests that are closed rather than open (Scott 1992). Evaluators of a given actor in a closed system are merely the other actors in the system, e.g., peers. Of course, not all tournaments have as their only audience members an internal pool of actors. What if by unleashing a superstar in an elite, and hence highly visible system can draw upon resources that are initially external to the system?

16 High and Low status (Open and Closed) systems C F,it ( Q ) it = kq a it A!b!c i S it n " i=1 k it = 1 / exp(s it / S it )!,where gamma proxies for the status of the tournament itself. Tournament participants enjoy lower costs to the extent that they both dominate the pool of internally available status and compete in a high-status contest (complete with an external audience who is willing to supply an inflow of further resources from the outside).

17 Results: In order to maximize social welfare (~ surplus) Optimal for open-system, elite tournaments that (like top laboratories or universities) may rivet the attention and attract resources from a relevant external audience. Optimal for closed-system, non-elite tournaments that do not attract attention and resources from a relevant external audience.! Allocation of Resources

18 An empirical extension. Colleges and Universities in the state of California,

19 An empirical extension. Measure of Matthew/Mark -- Salary Dispersion Measure of Status -- U.S. News and World Report Selectivity (1-5) Ratings

20 Does system status have an effect on Matthew vs. Mark? ln(d i,t +1 ) =! ln(d it ) + "S it +#M it + $ t +1 + % i,t +1

21 Does system status have an effect on Matthew vs. Mark? Yes. Higher status universities experience greater rates of salary dispersion not too surprising here. 1 -> 5 corresponds to 5% increase in the rate.

22 Does status of system have an effect on the efficacy of Matthew vs. Mark? S i,t +1 =!S it + " ln(d it ) + #S it ln(d it ) + +$M it + % t +1 + & i,t +1

23 (! S it )ln(d it ) Yes. High dispersion (Matthew Effect) has a positive effect on future status (welfare) for high status universities.

24 The LBS Doctoral Conference. Rising gamma? From: Subject: Date: To: Call for representatives: The 8th annual Trans-Atlantic Doctoral Conference April 30, :54:17 AM CDT Dear Trans-Atlantic Doctoral Conference participants, This year we are introducing a Best Paper Award. In each of the three areas (Accounting, Economics & Finance; Management Science; Management & Organization) a selection committee will select a paper that will receive the Best Paper Award and a paper that will receive the Best Paper Finalist Award.