Choosing a Strictly Proper Scoring Rule

AbstractWe empirically investigate incumbents’ and entrants’ bids on an original dataset of 192 scoring rule auctions for canteen services in Italy. Our findings show that winning rebates are lower (i.e., prices paid by the public buyer are higher) when the contract is awarded to the incumbent supplier. This result is not explained by the observable characteristics of the auction or the service awarded. We develop a simple theoretical model showing that the result is consistent with a setting in which the buyer exploits specific information on the incumbent supplier’s production cost.

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Evaluating probabilistic forecasts of football matches: the case against the ranked probability score

Journal of Quantitative Analysis in Sports ◽

10.1515/jqas-2019-0089 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Edward Wheatcroft

Keyword(s):

Scoring Rules ◽

Brier Score ◽

Sporting Events ◽

Forecast Performance ◽

Scoring Rule ◽

Probability Score ◽

Probabilistic Forecasts ◽

Non Local ◽

Evaluating Forecasts ◽

Non Locality

Abstract A scoring rule is a function of a probabilistic forecast and a corresponding outcome used to evaluate forecast performance. There is some debate as to which scoring rules are most appropriate for evaluating forecasts of sporting events. This paper focuses on forecasts of the outcomes of football matches. The ranked probability score (RPS) is often recommended since it is ‘sensitive to distance’, that is it takes into account the ordering in the outcomes (a home win is ‘closer’ to a draw than it is to an away win). In this paper, this reasoning is disputed on the basis that it adds nothing in terms of the usual aims of using scoring rules. A local scoring rule is one that only takes the probability placed on the outcome into consideration. Two simulation experiments are carried out to compare the performance of the RPS, which is non-local and sensitive to distance, the Brier score, which is non-local and insensitive to distance, and the Ignorance score, which is local and insensitive to distance. The Ignorance score outperforms both the RPS and the Brier score, casting doubt on the value of non-locality and sensitivity to distance as properties of scoring rules in this context.

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Characterising scoring rules by their solution in iteratively undominated strategies

Economic Theory ◽

10.1007/s00199-021-01353-w ◽

2021 ◽

Author(s):

Christian Basteck

Keyword(s):

Monotonicity Property ◽

Scoring Rules ◽

The Other ◽

Approval Voting ◽

Property A ◽

Borda Rule ◽

Scoring Rule ◽

Direct Mechanism ◽

Social Choice Correspondence ◽

Choice Correspondence

AbstractWe characterize voting procedures according to the social choice correspondence they implement when voters cast ballots strategically, applying iteratively undominated strategies. In elections with three candidates, the Borda Rule is the unique positional scoring rule that satisfies unanimity (U) (i.e., elects a candidate whenever it is unanimously preferred) and is majoritarian after eliminating a worst candidate (MEW)(i.e., if there is a unanimously disliked candidate, the majority-preferred among the other two is elected). In a larger class of rules, Approval Voting is characterized by a single axiom that implies both U and MEW but is weaker than Condorcet-consistency (CON)—it is the only direct mechanism scoring rule that is majoritarian after eliminating a Pareto-dominated candidate (MEPD)(i.e., if there is a Pareto-dominated candidate, the majority-preferred among the other two is elected); among all finite scoring rules that satisfy MEPD, Approval Voting is the most decisive. However, it fails a desirable monotonicity property: a candidate that is elected for some preference profile, may lose the election once she gains further in popularity. In contrast, the Borda Rule is the unique direct mechanism scoring rule that satisfies U, MEW and monotonicity (MON). There exists no direct mechanism scoring rule that satisfies both MEPD and MON and no finite scoring rule satisfying CON.

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The Hyvärinen scoring rule in Gaussian linear time series models

Journal of Statistical Planning and Inference ◽

10.1016/j.jspi.2020.08.004 ◽

2021 ◽

Vol 212 ◽

pp. 126-140

Author(s):

Silvia Columbu ◽

Valentina Mameli ◽

Monica Musio ◽

Philip Dawid

Keyword(s):

Time Series ◽

Linear Time ◽

Time Series Models ◽

Scoring Rule

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When does risk outweigh reward? Identifying potential scoring strategies with netballs new two-point rule

10.31236/osf.io/9wydp ◽

2020 ◽

Author(s):

Aaron Fox ◽

Lyndell Bruce

Keyword(s):

Scoring Rule ◽

Potential Use

This preprint examines a series of questions surrounding the implementation and potential use of the new two-point scoring rule in the upcoming 2020 season of Australia's national netball competition (i.e. Suncorp Super Netball).

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