Abstract
Equality of opportunity is usually defined as a situation where the effect of circumstances on outcome is nullified (compensation principle) and effort is rewarded (reward principle). We propose a new version of the reward principle based on the idea that effort deserves reward for it is costly. We show that luck can be introduced in two ways in the definition of these principles, depending on whether the correlation between luck and circumstances should be nullified and whether the correlation between luck and effort should be rewarded. In this regard, the timing of luck with respect to effort decisions is crucial, as is exemplified by moral hazard where effort choice influences the lottery of future uncertain events.
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Notes
Frank (2016).
Of course, the principle is meaningless if society does not value the outcome realized with effort as input. Thus in the background, the outcome introduced in Sect. 2.2 below is assumed to be of value to all individuals and then to society.
If work duration is statutory and differs across firms, it can be said that it is a circumstance. It should be compensated and in fact the cost of working more should be more compensated than the cost of working less. The principle of compensation can be useful if there is full cardinality and comparability of the cost of effort.
We will later signal the rare instances where the assumption of a metric space is required.
In the rest, for notational simplicity, we omit this adjustment.
Some may contend that the pure pleasure of gambling remains intact even if outcomes are equalized ex post. However, casual empiricism suggests that the thrill of poker games is higher when monetary gains are at stake, compared to high-school games where the only stake is a handful of matchsticks.
Of course, one may contend that the tax treatment of gambling gains does not simply reflect collective preference for redistribution but also reflects the government’s objective to provide incentives to participate in revenue-generating gambling.
In fact, such positions might echo the previous discussion on the preference for skewness in gambling contexts: the asymmetric compensation for luck would lead to a skewed distribution of the consequences of genetic luck that would be welfare enhancing, from the ex-ante perspective where genetic endowments have not been drawn.
Strictly speaking, introducing distribution functions and cumulative distribution functions, as we do here, presupposes that the set \({\mathcal {L}}^r\) be a metric space. We make this assumption for ease of notations. However, the results derived below could generalize easily to the case where \({\mathcal {L}}^r\) is not a metric space by using Dirac mass distributions on the universe of luck.
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Acknowledgements
We are grateful to Marc Fleurbaey and two anonymous referees for useful suggestions. Lefranc acknowledges the support of the project Labex MME-DII (ANR11-LBX-0023-01).
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Lefranc, A., Trannoy, A. Equality of opportunity, moral hazard and the timing of luck. Soc Choice Welf 49, 469–497 (2017). https://doi.org/10.1007/s00355-017-1054-8
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DOI: https://doi.org/10.1007/s00355-017-1054-8