A Note on Sandroni-Shmaya Belief Elicitation Mechanism

2017 ◽  
Vol 10 (2) ◽  
pp. 14-21 ◽  
Author(s):  
Arthur Carvalho
Keyword(s):  
Economic Theory ◽  
Scoring Rules ◽  
Risk Attitudes ◽  
Risk And Uncertainty ◽  
Proper Scoring Rules ◽  
Incentive Compatible ◽  
Decisions Under Risk ◽  
Belief Elicitation ◽  
Proper Scoring Rule ◽  
Extra Assumption

Incentive-compatible methods for eliciting beliefs, such as proper scoring rules, often rely on strong assumptions about how humans behave when making decisions under risk and uncertainty. For example, standard proper scoring rules assume that humans are risk neutral, an assumption that is often violated in practice. Under such an assumption, proper scoring rules induce honest reporting of beliefs, in a sense that experts maximize their expected scores from a proper scoring rule by honestly reporting their beliefs.Sandroni and Shmaya [Economic Theory Bulletin, volume 1, issue 1, 2013] suggested a remarkable mechanism based on proper scoring rules that induces honest reporting of beliefs without any assumptions on experts’ risk attitudes. In particular, the authors claimed that the mechanism relies only on the natural assumptions of probabilistic sophistication and dominance. We suggest in this paper that the reduction of compound lotteries axiom is another assumption required for Sandroni and Shmaya’s mechanism to induce honest reporting of beliefs. We further elaborate on the implications of such an extra assumption in light of recent findings regarding the reduction of compound lotteries axiom.

scholarly journals A Truth Serum for Non-Bayesians: Correcting Proper Scoring Rules for Risk Attitudes

2009 ◽  
Vol 76 (4) ◽  
pp. 1461-1489 ◽  
Author(s):  
THEO OFFERMAN ◽  
JOEP SONNEMANS ◽  
GIJS VAN DE KUILEN ◽  
PETER P. WAKKER
Keyword(s):  
Scoring Rules ◽  
Risk Attitudes ◽  
Proper Scoring Rules

scholarly journals An Equivalence between Wagering and Fair-Division Mechanisms

2019 ◽  
Vol 33 ◽  
pp. 1957-1964
Author(s):  
Rupert Freeman ◽  
David M. Pennock ◽  
Jennifer Wortman Vaughan
Keyword(s):  
Time Allocation ◽  
Fair Division ◽  
Scoring Rules ◽  
Fair Allocation ◽  
Future Event ◽  
Proper Scoring Rules ◽  
Incentive Compatible ◽  
Divisible Goods ◽  
Financial Securities ◽  
Division Mechanism

We draw a surprising and direct mathematical equivalence between the class of allocation mechanisms for divisible goods studied in the context of fair division and the class of weakly budget-balanced wagering mechanisms designed for eliciting probabilities. The equivalence rests on the intuition that wagering is an allocation of financial securities among bettors, with a bettor’s value for each security proportional to her belief about the likelihood of a future event. The equivalence leads to theoretical advances and new practical approaches for both fair division and wagering. Known wagering mechanisms based on proper scoring rules yield fair allocation mechanisms with desirable properties, including the first strictly incentive compatible fair-division mechanism. At the same time, allocation mechanisms make for novel wagering rules, including one that requires only ordinal uncertainty judgments and one that outperforms existing rules in a range of simulations.

The Behavioral Consequences of Conflict Exposure on Risk Preferences

2021 ◽  
Author(s):  
Enrique Fatas ◽  
Nathaly Jiménez ◽  
Lina Restrepo-Plaza ◽  
Gustavo Rincón
Keyword(s):  
Substantial Effect ◽  
Risk Attitudes ◽  
Behavioral Consequences ◽  
Criminal Violence ◽  
Incentive Compatible ◽  
Attitudinal Factors ◽  
Different Types ◽  
Close Relatives ◽  
Different Sources ◽  
Consequences Of Violence

Violent conflict is a polyhedric phenomenon. Beyond the destruction of physical and human capital and the economic, political, and social costs war generates, there is an additional burden carried by victims: persistent changes in the way they make decisions. Exposure to violence generates changes in how individuals perceive other individuals from their group and other groups, how they discount the future, and how they assess and tolerate risk. The behavioral consequences of violence exposure can be documented using experiments in which participants make decisions in a controlled, incentive-compatible scenario. The external validity of experiments is reinforced when the studies are run in postconflict scenarios, for example, in Colombia, with real victims of conflict. The experimental tasks, therefore, may map risk attitudes among victims and nonvictims of the conflict who share a common background, and distinguish between different types of exposure (direct versus indirect) and different sources of violence (conflict-related versus criminal violence). The experimental evidence collected in Colombia is consistent with a long-lasting and substantial effect of conflict exposure on risk attitudes. Victims are more likely to take risks and less likely to make safe choices than nonvictims, controlling for demographic, socioeconomic, and attitudinal factors. The effect is significant only when the source of violence is conflict (exerted by guerrilla or paramilitary militias) and when violence is experienced directly by individuals. Indirect conflict exposure (suffered by close relatives) and criminal violence leave no significant mark on participants’ risk attitudes in the study.

Decisions and Proper Scoring Rules

2008 ◽  
pp. 15-26
Author(s):  
Bruno de Finetti ◽  
Maria Carla Galavotti ◽  
Hykel Hosni ◽  
Alberto Mura
Keyword(s):  
Scoring Rules ◽  
Proper Scoring Rules

scholarly journals Discrete Arrow–Pratt indexes for risk and uncertainty

2020 ◽  
Author(s):  
Aurélien Baillon ◽  
Olivier L’Haridon
Keyword(s):  
Gold Standard ◽  
Decision Models ◽  
Risk Attitudes ◽  
Choice Data ◽  
Risk And Uncertainty ◽  
Multiple Priors ◽  
Probability Transformation ◽  
Non Parametric

Abstract The Arrow–Pratt index, a gold standard in studies of risk attitudes, is not directly observable from choice data. Existing methods to measure it rely on parametric assumptions. We introduce a discrete Arrow–Pratt index, and its relative counterpart, that can be directly obtained from choices. Our approach is general: it is (i) non-parametric, (ii) applicable to both risk and uncertainty, (iii) and robust to probability transformation, non-additive beliefs and multiple priors. Our index can also be used to characterize various decision models through various simple consistency requirements. We analyze its properties and demonstrate how it can be measured.

On proper scoring rules and cumulative prospect theory

2018 ◽  
Vol 6 (3-4) ◽  
pp. 343-376 ◽  
Author(s):  
Arthur Carvalho ◽  
Stanko Dimitrov ◽  
Kate Larson
Keyword(s):  
Prospect Theory ◽  
Cumulative Prospect Theory ◽  
Scoring Rules ◽  
Proper Scoring Rules
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