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.

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.

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

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

scholarly journals Bayesian Model Selection Based on Proper Scoring Rules

2015 ◽  
Vol 10 (2) ◽  
pp. 479-499 ◽  
Author(s):  
A. Philip Dawid ◽  
Monica Musio
Keyword(s):  
Model Selection ◽  
Bayesian Model ◽  
Bayesian Model Selection ◽  
Scoring Rules ◽  
Proper Scoring Rules

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

Deepness of response: A quantitative analysis of its impact on post-progression survival time after first-line treatment in patients with mCRC.

2013 ◽  
Vol 31 (4_suppl) ◽  
pp. 427-427 ◽  
Author(s):  
Ulrich Robert Mansmann ◽  
Ute Sartorius ◽  
Ruediger Paul Laubender ◽  
Clemens Albrecht Giessen ◽  
Regina Esser ◽  
...  
Keyword(s):  
Outcome Measure ◽  
Joint Model ◽  
Scoring Rules ◽  
Significant Prognostic Factor ◽  
Tumor Shrinkage ◽  
Term Survival ◽  
Proper Scoring Rules ◽  
Efficacy Outcome ◽  
Tumor Load ◽  
The Impact

427 Background: The extent of tumor shrinkage in patients (pts) receiving chemotherapy +/- monoclonal antibodies has prognostic value for PFS and OS. "Deepness of response (DpR)" is a new efficacy outcome measure that could explain the impact of tumor shrinkage on long-term survival outcome. If shrinkage takes place DpR is the percentage of tumor shrinkage observed at the nadir compared to baseline. DpR is 0 for no change and negative if the tumor load increases. Longest diameter (LD) based on RECIST or a calculated tumor volume (ASCO GI 2012 #635) can quantify the tumor load at distinct time points. A joint model was presented (ASCO GI 2012 #580, ASCO 2012 #3603) which allows us to relate DpR to individual post-progression survival (PPS) time. Methods: Based on the data from 2 randomized trials (CRYSTAL, n=1198; OPUS, n=337), 4 treatment regimens (FOLFIRI +/- cetuximab and FOLFOX4 +/- cetuximab) were studied. A joint model was used to quantify individual changes in tumor size over time and to relate these changes to PFS and OS. Relationships between baseline tumor load and DpR and PPS were studied. Proper scoring rules were used to assess whether the LD-based or the volume-based approach allowed a better prediction of individual prognosis. Results: Results are reported for the CRYSTAL study using LD-based measures for 663 pts with KRAS wild-type tumors and imaging data. The 348 pts treated with FOLFIRI alone had a mean DpR of 35.52% (Interquartile range [IR]:12.09%, 59.86%), minimum DpR -80%. The 315 pts treated with FOLFIRI + cetuximab had a mean DpR of 50.07% (IR: 22.87%, 79.55%) and a minimum DpR of -49%. The DpR was significantly different between the 2 groups (p<0.00001). Individual DpR is a significant prognostic factor for PPS time in both the LD-based (p=0.0023) and volume-based (p=0.0003) models. Proper scoring rules provided evidence of a more precise estimation of individual PPS time based on volume algorithm-measured DpR. Results of the OPUS study will be presented. Conclusions: Our results emphasize the value of the variable DpR as a new efficacy outcome measure for clinical trials. The tumor-shrinking capacity of cetuximab was shown to be associated with its ability to prolong PPS.

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