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Unformatted text preview: 6.207/14.15: Networks Lecture 24: Decisions in Groups Daron Acemoglu and Asu Ozdaglar MIT December 9, 2009 1 Networks: Lecture 24 Introduction Outline Group and collective choices Arrow’s Impossibility Theorem GibbardSatterthwaite Impossibility Theorem Single peaked preferences and aggregation Group decisions under incomplete information Reading: EK, Chapter 23 Osborne, Chapter 9.7 2 1 2 Networks: Lecture 24 Group and Collective Choices Collective Choices: Introduction How do we think of a group making a collective decision? This presupposes some “mechanism” for example, bargaining or voting. Key question: Will a group make fair, correct and eﬃcient decisions? Two sets of issues: Aggregating up to collective preferences from individual preferences. Using dispersed information of the group eﬃciently. 3 Networks: Lecture 24 Group and Collective Choices Setup Abstract economy consisting of a finite set of individuals H , with the number of individuals denoted by H . Individual i ∈ H has an indirect utility function defined over choices available to the group or “policies” p ∈ P U ( p ; α i ) , where α i indexes the utility function (i.e., U ( p ; α i ) = U i ( p )). The bliss point of individual i is defined as: p ( α i ) = arg max U ( p ; α i ) . p ∈P 4 Networks: Lecture 24 Group and Collective Choices Preferences More Generally Individual i weakly prefers p to p , p i p and if he has a strict preference, p i p . Assume: completeness , reﬂexivity and transitivity (so that z i z and z i z implies z i z ). 5 Networks: Lecture 24 Group and Collective Choices Collective Preferences? Key question: Does there exist welfare function U S ( p ) that ranks policies for this group (or society)? Let us first start with a simple way of “aggregating” the preferences of individuals in the group: majoritarian voting . This will lead to the Condorcet paradox . 6 Networks: Lecture 24 Voting and the Condorcet Paradox The Condorcet Paradox Imagine a group consisting of three individuals, 1, 2, and 3, three choices and preferences 1 a c b 2 b a c 3 c b a Assume “open agenda direct democracy” system for making decisions within this group. A1. Direct democracy. The citizens themselves make the policy choices via majoritarian voting. A2. Sincere voting. Individuals vote “truthfully” rather than strategically. A3. Open agenda. Citizens vote over pairs of policy alternatives, such that the winning policy in one round is posed against a new alternative in the next round and the set of alternatives includes all feasible policies. What will happen? 7 Networks: Lecture 24 Voting and the Condorcet Paradox The Condorcet Paradox It can be verified that b will obtain a majority against a ....
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This note was uploaded on 06/12/2010 for the course EECS 6.207J taught by Professor Acemoglu during the Fall '09 term at MIT.
 Fall '09
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