Aggregating infinitely many probability measures
The problem of how to rationally aggregate probability measures occurs in particular (i) when a group of agents, each holding probabilistic beliefs, needs to rationalise a collective decision on the basis of a single ‘aggregate belief system’ and (ii) when an individual whose belief system is compat...
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| description | The problem of how to rationally aggregate probability measures occurs in particular (i) when a group of agents, each holding probabilistic beliefs, needs to rationalise a collective decision on the basis of a single ‘aggregate belief system’ and (ii) when an individual whose belief system is compatible with several (possibly infinitely many) probability measures wishes to evaluate her options on the basis of a single aggregate prior via classical expected utility theory (a psychologically plausible account of individual decisions). We investigate this problem by first recalling some negative results from preference and judgment aggregation theory which show that the aggregate of several probability measures should not be conceived as the probability measure induced by the aggregate of the corresponding expected utility preferences. We describe how McConway’s (Journal of the American Statistical Association, 76(374):410–414,
1981
) theory of probabilistic opinion pooling can be generalised to cover the case of the aggregation of infinite profiles of finitely additive probability measures, too; we prove the existence of aggregation functionals satisfying responsiveness axioms
à la
McConway plus additional desiderata even for infinite electorates. On the basis of the theory of propositional-attitude aggregation, we argue that this is the most natural aggregation theory for probability measures. Our aggregation functionals for the case of infinite electorates are neither oligarchic nor integral-based and satisfy (at least) a weak anonymity condition. The delicate set-theoretic status of integral-based aggregation functionals for infinite electorates is discussed. |
| doi_str_mv | 10.1007/s11238-014-9424-5 |
| format | Article |
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1981
) theory of probabilistic opinion pooling can be generalised to cover the case of the aggregation of infinite profiles of finitely additive probability measures, too; we prove the existence of aggregation functionals satisfying responsiveness axioms
à la
McConway plus additional desiderata even for infinite electorates. On the basis of the theory of propositional-attitude aggregation, we argue that this is the most natural aggregation theory for probability measures. Our aggregation functionals for the case of infinite electorates are neither oligarchic nor integral-based and satisfy (at least) a weak anonymity condition. The delicate set-theoretic status of integral-based aggregation functionals for infinite electorates is discussed.</description><identifier>ISSN: 0040-5833</identifier><identifier>EISSN: 1573-7187</identifier><identifier>DOI: 10.1007/s11238-014-9424-5</identifier><language>eng</language><publisher>Boston: Springer US</publisher><subject>Agglomeration ; Aggregates ; Analysis ; Axiomatization ; Axioms ; Behavioral/Experimental Economics ; Beliefs ; Compatibility ; Decision making ; Decision theory ; Economic Theory/Quantitative Economics/Mathematical Methods ; Economics ; Economics and Finance ; Electorate ; Entropy ; Epistemology ; Expected utility ; Finance ; Functionals ; Game Theory ; Insurance ; Judgement ; Management ; Motivation ; Operations Research/Decision Theory ; Preferences ; Probabilistic methods ; Probability ; Probability theory ; Social and Behav. Sciences ; Statistics for Business ; Studies ; Utilities ; Utility theory</subject><ispartof>Theory and decision, 2015-02, Vol.78 (2), p.319-337</ispartof><rights>Springer Science+Business Media New York 2014</rights><rights>Springer Science+Business Media New York 2015</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c559t-70d46c6982961d05804884754950ff41cb9230e46e0bd7d4f428de414b498413</citedby><cites>FETCH-LOGICAL-c559t-70d46c6982961d05804884754950ff41cb9230e46e0bd7d4f428de414b498413</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11238-014-9424-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11238-014-9424-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51298</link.rule.ids></links><search><creatorcontrib>Herzberg, Frederik</creatorcontrib><title>Aggregating infinitely many probability measures</title><title>Theory and decision</title><addtitle>Theory Decis</addtitle><description>The problem of how to rationally aggregate probability measures occurs in particular (i) when a group of agents, each holding probabilistic beliefs, needs to rationalise a collective decision on the basis of a single ‘aggregate belief system’ and (ii) when an individual whose belief system is compatible with several (possibly infinitely many) probability measures wishes to evaluate her options on the basis of a single aggregate prior via classical expected utility theory (a psychologically plausible account of individual decisions). We investigate this problem by first recalling some negative results from preference and judgment aggregation theory which show that the aggregate of several probability measures should not be conceived as the probability measure induced by the aggregate of the corresponding expected utility preferences. We describe how McConway’s (Journal of the American Statistical Association, 76(374):410–414,
1981
) theory of probabilistic opinion pooling can be generalised to cover the case of the aggregation of infinite profiles of finitely additive probability measures, too; we prove the existence of aggregation functionals satisfying responsiveness axioms
à la
McConway plus additional desiderata even for infinite electorates. On the basis of the theory of propositional-attitude aggregation, we argue that this is the most natural aggregation theory for probability measures. Our aggregation functionals for the case of infinite electorates are neither oligarchic nor integral-based and satisfy (at least) a weak anonymity condition. The delicate set-theoretic status of integral-based aggregation functionals for infinite electorates is discussed.</description><subject>Agglomeration</subject><subject>Aggregates</subject><subject>Analysis</subject><subject>Axiomatization</subject><subject>Axioms</subject><subject>Behavioral/Experimental Economics</subject><subject>Beliefs</subject><subject>Compatibility</subject><subject>Decision making</subject><subject>Decision theory</subject><subject>Economic Theory/Quantitative Economics/Mathematical Methods</subject><subject>Economics</subject><subject>Economics and Finance</subject><subject>Electorate</subject><subject>Entropy</subject><subject>Epistemology</subject><subject>Expected utility</subject><subject>Finance</subject><subject>Functionals</subject><subject>Game Theory</subject><subject>Insurance</subject><subject>Judgement</subject><subject>Management</subject><subject>Motivation</subject><subject>Operations Research/Decision Theory</subject><subject>Preferences</subject><subject>Probabilistic methods</subject><subject>Probability</subject><subject>Probability theory</subject><subject>Social and Behav. 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Sciences</topic><topic>Statistics for Business</topic><topic>Studies</topic><topic>Utilities</topic><topic>Utility theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Herzberg, Frederik</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Social Sciences Premium Collection</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Psychology Database (Alumni)</collection><collection>Social Science Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>International Bibliography of the Social Sciences (IBSS)</collection><collection>Technology Research 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One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest One Psychology</collection><collection>Engineering Collection</collection><collection>ABI/INFORM Collection China</collection><collection>ProQuest Central Basic</collection><jtitle>Theory and decision</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Herzberg, Frederik</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Aggregating infinitely many probability measures</atitle><jtitle>Theory and decision</jtitle><stitle>Theory Decis</stitle><date>2015-02-01</date><risdate>2015</risdate><volume>78</volume><issue>2</issue><spage>319</spage><epage>337</epage><pages>319-337</pages><issn>0040-5833</issn><eissn>1573-7187</eissn><abstract>The problem of how to rationally aggregate probability measures occurs in particular (i) when a group of agents, each holding probabilistic beliefs, needs to rationalise a collective decision on the basis of a single ‘aggregate belief system’ and (ii) when an individual whose belief system is compatible with several (possibly infinitely many) probability measures wishes to evaluate her options on the basis of a single aggregate prior via classical expected utility theory (a psychologically plausible account of individual decisions). We investigate this problem by first recalling some negative results from preference and judgment aggregation theory which show that the aggregate of several probability measures should not be conceived as the probability measure induced by the aggregate of the corresponding expected utility preferences. We describe how McConway’s (Journal of the American Statistical Association, 76(374):410–414,
1981
) theory of probabilistic opinion pooling can be generalised to cover the case of the aggregation of infinite profiles of finitely additive probability measures, too; we prove the existence of aggregation functionals satisfying responsiveness axioms
à la
McConway plus additional desiderata even for infinite electorates. On the basis of the theory of propositional-attitude aggregation, we argue that this is the most natural aggregation theory for probability measures. Our aggregation functionals for the case of infinite electorates are neither oligarchic nor integral-based and satisfy (at least) a weak anonymity condition. The delicate set-theoretic status of integral-based aggregation functionals for infinite electorates is discussed.</abstract><cop>Boston</cop><pub>Springer US</pub><doi>10.1007/s11238-014-9424-5</doi><tpages>19</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Agglomeration Aggregates Analysis Axiomatization Axioms Behavioral/Experimental Economics Beliefs Compatibility Decision making Decision theory Economic Theory/Quantitative Economics/Mathematical Methods Economics Economics and Finance Electorate Entropy Epistemology Expected utility Finance Functionals Game Theory Insurance Judgement Management Motivation Operations Research/Decision Theory Preferences Probabilistic methods Probability Probability theory Social and Behav. Sciences Statistics for Business Studies Utilities Utility theory |
| title | Aggregating infinitely many probability measures |
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