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Essays on Strategy-proof Social Choice

Reffgen, Alexander LU (2011) In Lund Economic Studies 164.
Abstract (Swedish)
Popular Abstract in Swedish

Denna avhandling ger ett bidrag till teorin om strategisäkra kollektiva beslut. I denna teori undersöks under vilka förutsättningar det är möjligt att konstruera omröstningsprocedurer (hädanefter kallade för kollektiva valfunktioner) som är strategisäkra i den bemärkelsen att ingen väljare kan ändra utfallet av en omröstning till sin fördel genom att inte rösta enligt sina sanna preferenser, det vill säga en strategisäker kollektiv valfunktion ger aldrig några incitament till strategiskt röstande. Avhandlingen består av tre separata uppsatser som under olika teoretiska förutsättningar presenterar fullständiga karakteriseringar av de strategisäkra kollektiva valfunktionerna.



Den... (More)
Popular Abstract in Swedish

Denna avhandling ger ett bidrag till teorin om strategisäkra kollektiva beslut. I denna teori undersöks under vilka förutsättningar det är möjligt att konstruera omröstningsprocedurer (hädanefter kallade för kollektiva valfunktioner) som är strategisäkra i den bemärkelsen att ingen väljare kan ändra utfallet av en omröstning till sin fördel genom att inte rösta enligt sina sanna preferenser, det vill säga en strategisäker kollektiv valfunktion ger aldrig några incitament till strategiskt röstande. Avhandlingen består av tre separata uppsatser som under olika teoretiska förutsättningar presenterar fullständiga karakteriseringar av de strategisäkra kollektiva valfunktionerna.



Den första uppsatsen, ”Generalizing the Gibbard-Satterthwaite theorem: partial preferences, the degree of manipulation, and multi-valuedness”, har sin utgångspunkt i det så kallade Gibbard-Satterthwaite teoremet, som betraktas som det fundamentala resultatet i teorin om strategisäkra kollektiva beslut. Detta teorem säger att om det finns minst tre alternativ av vilka exakt ett ska väljas, så är en kollektiv valfunktion strategisäker om och endast om den är diktatorisk, det vill säga en väljare bestämmer enväldigt över omröstningens utfall. Detta resultat generaliseras på tre sätt: För det första visas att väljarnas preferenser inte behöver vara fullständiga för att härleda teoremets slutsats, utan teoremet gäller även om väljarnas preferenser tillhör en lämplig klass av partiella preferenser. För det andra visas att en kollektiv valfunktion som inte är diktatorisk, och därmed inte heller strategisäker, kan manipuleras på ett sådant sätt att någon väljare genom strategisk röstning kan ändra omröstningens utfall till sitt bästa eller nästbästa alternativ. För det tredje visas en variant av teoremet som generaliserar villkoret att exakt ett alternativ väljs, och antalet valda alternativ är nu ett godtyckligt, men i förväg bestämt heltal.



I den andra uppsatsen, ”Strategy-proof voting for multiple public goods” (samförfattad med Lars-Gunnar Svensson), betraktas en omröstningsmodell i vilken det finns flera kategorier av alternativ och från varje kategori ska ett alternativ väljas under bivillkoret att vissa kombinationer av alternativ inte är valbara. För denna omröstningsmodell karakteriseras mängden av alla strategisäkra kollektiva valfunktioner för tre olika domäner av preferenser över produktmängden av de olika kategorierna, nämligen för additiva preferenser, fullständigt separabla preferenser och svagt separabla preferenser.



Den tredje uppsatsen, “Strategy-proof social choice on multiple single-peaked domains and preferences for parties”, har sin utgångspunkt i så kallade domäner av entoppiga preferenser som spelar en viktig roll inom teorin för strategisäkra kollektiva beslut eftersom det existerar en stor klass av icke-diktatoriska strategisäkra kollektiva valfunktioner på dessa preferensdomäner. Dessa domäner av entoppiga preferenser generaliseras till multipla domäner av entoppiga preferenser som har flera underliggande ordningar med avseende på vilka en preferens kan vara entoppig. Huvudresultatet i uppsatsen ger en fullständig karakterisering av de strategisäkra kollektiva valfunktionerna på multipla domäner av entoppiga preferenser. Vidare visas också i en spatial omröstningsmodell att preferenser över partier lämpligen kan representeras av multipla domäner av entoppiga preferenser. (Less)
Abstract
This thesis makes a contribution to strategy-proof social choice theory, in which one investigates the conditions under which it is possible to construct social choice functions (i.e., voting procedures) that can never be manipulated in the sense that some voter, by misrepresentation of his true preferences, can change the outcome of a voting and obtain an alternative he prefers to the one that honest voting would give. The thesis consists of three separate essays, which provide complete characterizations of the strategy-proof social choice functions in different formal frameworks as described in the following.



The first essay, “Generalizing the Gibbard-Satterthwaite theorem: partial preferences, the degree of... (More)
This thesis makes a contribution to strategy-proof social choice theory, in which one investigates the conditions under which it is possible to construct social choice functions (i.e., voting procedures) that can never be manipulated in the sense that some voter, by misrepresentation of his true preferences, can change the outcome of a voting and obtain an alternative he prefers to the one that honest voting would give. The thesis consists of three separate essays, which provide complete characterizations of the strategy-proof social choice functions in different formal frameworks as described in the following.



The first essay, “Generalizing the Gibbard-Satterthwaite theorem: partial preferences, the degree of manipulation, and multi-valuedness”, has its starting point in the Gibbard-Satterthwaite theorem, which is the fundamental result of strategy-proof social choice theory. This result states that if exactly one alternative should be elected from a set of at least three eligible alternatives, then a social choice function is strategy-proof if and only if it is dictatorial. This result is generalized in three ways: First, we prove that the theorem is still valid when individual preferences belong to a convenient class of partial preferences. Second, we show that that every non-dictatorial surjective social choice function is not only manipulable, but can be manipulated in such a way that some individual obtains either his best or second best alternative. Third, we prove a variant of the theorem where the outcomes of the social choice function are subsets of the set of alternatives of an a priori fixed size.



In the second essay, “Strategy-proof voting for multiple public goods” (co-authored with Lars-Gunnar Svensson), we consider a voting model where the set of feasible alternatives is a subset of a product set of several finite categories, and we characterize the set of all strategy-proof social choice functions for three different types of preference domains over the product set, namely for the domains of additive, completely separable, and weakly separable preferences.



The third essay, “Strategy-proof social choice on multiple single-peaked domains and preferences for parties”, starts from the concept of single-peaked domains, which play an important role in strategy-proof social choice theory because they admit a large class of non-dictatorial strategy-proof social choice functions. These domains are generalized to multiple single-peaked domains, where the set of alternatives is equipped with several underlying orderings with respect to which a preference can be single-peaked. The main result in this essay provides a complete characterization of the strategy-proof social choice functions on multiple single-peaked domains. We show also in the framework of a spatial voting model for party elections that multiple single-peaked domains are appropriate to represent preferences over parties. (Less)
Please use this url to cite or link to this publication:
author
supervisor
opponent
  • Weymark, John, Vanderbilt University
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Strategy-proofness, Social choice functions, Gibbard-Satterthwaite theorem, Restricted preference domains
in
Lund Economic Studies
volume
164
pages
120 pages
defense location
Holger Crafoords Ekonomicentrum, Sal EC3:211
defense date
2011-06-06 14:15
ISSN
0460-0029
language
English
LU publication?
yes
id
0b8837cc-804e-4334-9393-46b8cc2166f7 (old id 1962519)
date added to LUP
2011-05-16 11:33:47
date last changed
2016-09-19 08:45:00
@misc{0b8837cc-804e-4334-9393-46b8cc2166f7,
  abstract     = {This thesis makes a contribution to strategy-proof social choice theory, in which one investigates the conditions under which it is possible to construct social choice functions (i.e., voting procedures) that can never be manipulated in the sense that some voter, by misrepresentation of his true preferences, can change the outcome of a voting and obtain an alternative he prefers to the one that honest voting would give. The thesis consists of three separate essays, which provide complete characterizations of the strategy-proof social choice functions in different formal frameworks as described in the following.<br/><br>
<br/><br>
The first essay, “Generalizing the Gibbard-Satterthwaite theorem: partial preferences, the degree of manipulation, and multi-valuedness”, has its starting point in the Gibbard-Satterthwaite theorem, which is the fundamental result of strategy-proof social choice theory. This result states that if exactly one alternative should be elected from a set of at least three eligible alternatives, then a social choice function is strategy-proof if and only if it is dictatorial. This result is generalized in three ways: First, we prove that the theorem is still valid when individual preferences belong to a convenient class of partial preferences. Second, we show that that every non-dictatorial surjective social choice function is not only manipulable, but can be manipulated in such a way that some individual obtains either his best or second best alternative. Third, we prove a variant of the theorem where the outcomes of the social choice function are subsets of the set of alternatives of an a priori fixed size.<br/><br>
<br/><br>
In the second essay, “Strategy-proof voting for multiple public goods” (co-authored with Lars-Gunnar Svensson), we consider a voting model where the set of feasible alternatives is a subset of a product set of several finite categories, and we characterize the set of all strategy-proof social choice functions for three different types of preference domains over the product set, namely for the domains of additive, completely separable, and weakly separable preferences.<br/><br>
<br/><br>
The third essay, “Strategy-proof social choice on multiple single-peaked domains and preferences for parties”, starts from the concept of single-peaked domains, which play an important role in strategy-proof social choice theory because they admit a large class of non-dictatorial strategy-proof social choice functions. These domains are generalized to multiple single-peaked domains, where the set of alternatives is equipped with several underlying orderings with respect to which a preference can be single-peaked. The main result in this essay provides a complete characterization of the strategy-proof social choice functions on multiple single-peaked domains. We show also in the framework of a spatial voting model for party elections that multiple single-peaked domains are appropriate to represent preferences over parties.},
  author       = {Reffgen, Alexander},
  issn         = {0460-0029},
  keyword      = {Strategy-proofness,Social choice functions,Gibbard-Satterthwaite theorem,Restricted preference domains},
  language     = {eng},
  pages        = {120},
  series       = {Lund Economic Studies},
  title        = {Essays on Strategy-proof Social Choice},
  volume       = {164},
  year         = {2011},
}