Lottery Design Research Articles

How to Win the Lottery, Guaranteed: Ten Comments on Cushing and Stewart's Guaranteed-Win Minimal Lottery Design

How to Win the Lottery, Guaranteed: Ten Comments on Cushing and Stewart's Guaranteed-Win Minimal Lottery Design

The Effects of Charter High Schools on Academic Achievement and College Enrollment: Evidence from Los Angeles

Abstract This paper estimates the causal effects of enrollment in one of five oversubscribed high-quality Los Angeles charter schools using a lottery design. Enrolling in a charter school increased eleventh-grade standardized test scores and enrollment and persistence in four-year colleges substantially, but had no effect on high school GPA. Charter students took more advanced coursework, were less likely to skip class, were more likely to apply to a four-year college, and reported more teacher support for college-going. The increase in four-year persistence appears to be driven by more enrollment and persistence in University of California campuses, which have higher graduation rates than the likely alternatives. This suggests that the effects of charter schools could depend on the availability of high graduation rate colleges.

Lottery incentives for smoking cessation at the workplace: design and protocol of the smoke-free lottery - a cluster randomized trial

BackgroundSmoking is the leading behavioral risk factor for the loss of healthy life years. Many smokers want to quit, but have trouble doing so. Financial incentives in workplace settings have shown promising results in supporting smokers and their design influences their impact. Lotteries that leverage behavioral economic insights might improve the effectiveness of workplace cessation support.Methods and designWe examine in a cluster randomized trial if a workplace cessation group training paired with lottery deadlines will increase continuous abstinence rates over and above the cessation training alone. Organizations are randomized to either the control arm or lottery arm. The lotteries capitalize regret aversion by always informing winners at the deadline, but withholding prizes if they smoked. In the lottery-arm, winners are drawn out of all participants within a training group, regardless of their smoking status. In weeks 1-13 there are weekly lotteries. Winners are informed about their prize (€50), but can only claim it if they did not smoke that week, validated biochemically. After 26 weeks, there is a long-term lottery where the winners are informed about their prize (vacation voucher worth €400), but can only claim it if they were abstinent between weeks 13 and 26. The primary outcome is continuous abstinence 52 weeks after the quit date.DiscussionThere is a quest for incentives to support smoking cessation that are considered fair, affordable and effective across different socioeconomic groups. Previous use of behavioral economics in the design of lotteries have shown promising results in changing health behavior. This cluster randomized trial aims to demonstrate if these lotteries are also effective for supporting smoking cessation. Therefore the study design and protocol are described in detail in this paper. Findings might contribute to the application and development of effective cessation support at the workplace.Trial registrationNetherlands Trial Register Identifier: NL8463. Date of registration: 17-03-2020.

Immigration Lottery Design: Engineered and Coincidental Consequences of H-1B Reforms

Abstract The H-1B Visa Reform Act of 2004 dictates an annual allocation of 85,000 visas with 20,000 reserved for advanced-degree applicants. We represent the main requirements of this legislation as formal axioms and characterize visa allocation rules consistent with the axioms. Despite the precise number reserved, we show that the range of implementations satisfying these axioms can change the allocation of advanced-degree visas by as much as 14,000 in an average year. Of all rules satisfying these axioms, the 2019 rule imposed by executive order is most favorable to advanced-degree holders. However, two earlier modifications resulted in larger changes, potentially unintentionally.

Lottery Design for School Choice

This paper studies outcomes of the deferred acceptance algorithm in large random matching markets where priorities are generated either by a single lottery or by independent lotteries. In contrast to prior work, my model permits students to submit lists of varying lengths and schools to vary in their popularity and number of seats. In a limiting regime where the number of students and schools grow while the length of student lists and number of seats at each school remain bounded, I provide exact expressions for the number of students who list l schools and match to one of their top k choices, for each [Formula: see text]. These expressions provide three main insights. First, there is a persistent tradeoff between using a single lottery and independent lotteries. For students who submit short lists, the rank distribution under a single lottery stochastically dominates the corresponding distribution under independent lotteries. However, the students who submit the longest lists are always more likely to match when schools use independent lotteries. Second, I compare the total number of matches in the two lottery systems, and find that the shape of the list length distribution plays a key role. If this distribution has an increasing hazard rate, then independent lotteries match more students. If it has a decreasing hazard rate, the comparison reverses. To my knowledge, this is the first analytical result comparing the size of stable matchings under different priority rules. Finally, I study the fraction of assigned students who receive their first choice. Under independent lotteries, this fraction may be arbitrarily small, even if schools are equally popular. Under a single lottery, we provide a tight lower bound on this fraction which depends on the ratio r of the popularity of the most to least popular school. When each school has a single seat, the fraction of assigned students who receive their first choice is at least [Formula: see text]. This guarantee increases to [Formula: see text] as the number of seats at each school increases. This paper was accepted by Gabriel Weintraub, revenue management and market analytics. Supplemental Material: The data files and online appendix are available at https://doi.org/10.1287/mnsc.2022.4338 .

Excited and aroused: The predictive importance of simple choice process metrics.

We conduct a lottery experiment to assess the predictive importance of simple choice process metrics (SCPMs) in forecasting risky 50/50 gambling decisions using different types of machine learning algorithms as well as traditional choice modeling approaches. The SCPMs are recorded during a fixed pre-decision phase and are derived from tracking subjects’ eye movements, pupil sizes, skin conductance, and cardiovascular and respiratory signals. Our study demonstrates that SCPMs provide relevant information for predicting gambling decisions, but we do not find forecasting accuracy to be substantially affected by adding SCPMs to standard choice data. Instead, our results show that forecasting accuracy highly depends on differences in subject-specific risk preferences and is largely driven by including information on lottery design variables. As a key result, we find evidence for dynamic changes in the predictive importance of psychophysiological responses that appear to be linked to habituation and resource-depletion effects. Subjects’ willingness to gamble and choice-revealing arousal signals both decrease as the experiment progresses. Moreover, our findings highlight the importance of accounting for previous lottery payoff characteristics when investigating the role of emotions and cognitive bias in repeated decision-making scenarios.

The Near Miss Effect and the Framing of Lotteries

We present a framework for analyzing the near miss effect in lotteries. A decision maker (DM) facing a lottery, falsely interprets losing outcomes that are close to winning ones, as a sign that success is within reach. As a result of this false belief, the DM will prefer lotteries that induce a higher frequency of near misses, even if the underlying probability of winning is constant. We define a near miss index that measures the near miss effect induced by a given lottery and analyze the optimal lottery design in terms of near miss. This analysis leads us to establish a fruitful connection between our near miss framework and the field of coding theory. Building on this connection we compare different lottery frames and the near miss effect they induce. Analyzing an interaction between a seller and a buyer of lotteries allows us to gain further insight into the optimal framing of lotteries and might offer a potential explanation as to why lotteries with a very small probability of winning are commonplace and attractive.

The Optimal Design of State-Run Lotteries

The Optimal Design of State-Run Lotteries

Design of Lotteries and Wait-Lists for Affordable Housing Allocation

We study a setting in which dynamically arriving items are assigned to waiting agents, who have heterogeneous values for distinct items and heterogeneous outside options. An ideal match would both target items to agents with the worst outside options and match them to items for which they have high value. Our first finding is that two common approaches—using independent lotteries for each item and using a waitlist in which agents lose priority when they reject an offer—lead to identical outcomes in equilibrium. Both approaches encourage agents to accept items that are marginal fits. We show that the quality of the match can be improved by using a common lottery for all items. If participation costs are negligible, a common lottery is equivalent to several other mechanisms, such as limiting participants to a single lottery, using a waitlist in which offers can be rejected without punishment, or using artificial currency. However, when there are many agents with low need, there is an unavoidable trade-off between matching and targeting. In this case, utilitarian welfare may be maximized by focusing on good matching (if the outside option distribution is light tailed) or good targeting (if it is heavy tailed). Using a common lottery achieves near-optimal matching, whereas introducing participation costs achieves near-optimal targeting. This paper was accepted by Charles Corbett, operations management.

Effects of Household Shocks on Risk Preferences and Loss Aversion: Evidence from Upland Smallholders of South East Asia

Avoiding risk in financial decisions is credited to be a key contributor to persistent poverty and poverty traps. In spite of this, the methods used to measure behaviour under risk rarely reflect an adequate representation of the lives of smallholders in low income economies. We estimate risk preferences and their determinants by including two key aspects: aversion to losses and exposure to long term risk and vulnerability. We examine risk preferences of 93 smallholders in Cambodia and 91 smallholders in Lao PDR with an incentivised lottery design under the framework of Expected Utility Theory (EUT), Rank Dependent Utility Theory (RDU) and Cumulative Prospect Theory (CPT). We find that CPT best explains our data, but parameter values vary to those most commonly found in the literature. We report that the experience of household shocks have a significant effect on choice behaviour in the loss domain, even when we control for a large set of socio-economic and demographic variables.

Do lottery operators exploit their lottery power? Efficiency and equality considerations in optimal lottery design

We study the problem facing the operator of a lottery who is charged with raising revenue for the public finances. Demand for the lottery is a function of both disposable income and the pricing of the game. Departing from the current literature, we show that optimal lottery pricing includes corrections for the degree of inequality and skewness in the income distribution and features of the function relating lottery spend to disposable income. When gross lottery expenditure is regressive, it is optimal for the operator to improve the terms of the game by being more generous with the proportion of spend that is returned to players. The opposite result holds when gross lottery expenditure is progressive. Using results from analysis of the U.K. National Lottery’s Saturday game between 1997 and 2013, we show that the effective price was about ten percentage points too low to be efficient, so that the operator was not fully exploiting its lottery power. However, we also show that, were it to have raised its price to improve efficiency, it would have increased inequality.

Does It Pay to Buy the Pot in the Canadian 6/49 Lotto? Implications for Lottery Design

The Canadian 6/49 Lotto©, despite its unusual payout structure, is one of the few government sponsored lotteries that has the potential for a favourable strategy we call the pot. By the we mean that a syndicate buys one of each ticket in the lottery, ensuring that it holds a jackpot winner. We assume that the other bettors independently buy small numbers of tickets. This paper presents (1) a formula for the syndicate's expected return, (2) conditions under which buying the pot produces a significant positive expected return, and (3) the implications of these findings for lottery design.

Do Lottery Operators Exploit Their Lottery Power? Efficiency and Equality Considerations in Optimal Lottery Design

We study the problem facing the operator of a lottery who is charged with raising revenue for the public finances. Demand for the lottery is a function of both disposable income and the pricing of the game. Departing from the current literature, we show that optimal lottery pricing includes corrections for the degree of inequality and skewness in the income distribution and features of the function relating lottery spend to disposable income. When gross lottery expenditure is regressive, it is optimal for the operator to improve the terms of the game by being more generous with the proportion of spend that is returned to players. The opposite result holds when gross lottery expenditure is progressive. Using results from analysis of the U.K. National Lottery’s Saturday game between 1997 and 2013, we show that the effective price was about ten percentage points too low to be efficient, so that the operator was not fully exploiting its lottery power. However, we also show that, were it to have raised its price to improve efficiency, it would have increased inequality.

Does it Pay to Buy the Pot in the Canadian 6/49 Lottery? Implications for Lottery Design

The Canadian 6/49 Lotto, despite its unusual payout structure, is one of the few government sponsored lotteries that has the potential for a favorable strategy we call the pot. By the we mean that a syndicate buys one of each ticket in the lottery, ensuring that it holds a jackpot winner. We assume that the other bettors independently buy small numbers of tickets. This paper presents (1) a formula for the syndicate's expected return, (2) conditions under which buying the pot produces a significant positive expected return, and (3) the implications of these findings for lottery design.

Efficient lottery design

There has been a surge of interest in stochastic assignment mechanisms that have proven to be theoretically compelling thanks to their prominent welfare properties. Contrary to stochastic mechanisms, however, lottery mechanisms are commonly used in real life for indivisible goods allocation. To help facilitate the design of practical lottery mechanisms, we provide new tools for obtaining stochastic improvements in lotteries. As applications, we propose lottery mechanisms that improve upon the widely used random serial dictatorship mechanism and a lottery representation of its competitor, the probabilistic serial mechanism. The tools we provide here can be useful in developing welfare-enhanced new lottery mechanisms for practical applications such as school choice.

Optimal Lottery Design for Public Financing

This article develops a model of optimal lottery design for public financing, on the assumption that economic agents view buying lottery tickets as a form of entertainment. Given that lotteries are optimally designed, it offers two findings: (1) the fundraising potential of a lottery is independent of its type (specifically, of whether it is a fixed-prize type or a pari mutuel); and (2) the ratio of the optimal winning prize amount in each prize class to total lottery sales is equalised to the elasticity of demand for lottery ticket purchases with respect to the winning prize in each prize class.

USING LOTTERIES TO FINANCE PUBLIC GOODS: THEORY AND EXPERIMENTAL EVIDENCE*

This study explores the economics of charitable fund‐raising. We begin by developing theory that examines the optimal lottery design while explicitly relaxing both risk‐neutrality and preference homogeneity assumptions. We test our theory using a battery of experimental treatments and find that our theoretical predictions are largely confirmed. Specifically, we find that single‐ and multiple‐prize lotteries dominate the voluntary contribution mechanism both in total dollars raised and the number of contributors attracted. Moreover, we find that the optimal fund‐raising mechanism depends critically on the risk postures of potential contributors and preference heterogeneity.

An Economist’s Guide to Lottery Design

This paper outlines the issues relevant to the design of pari‐mutuel lottery games and makes inferences about game design effects from estimates of how rollovers affect sales. Lottery tickets sales depend positively on the proportion of revenue returned as prizes, positively on the skewness of the prize distribution (which depends largely on how much of the prize money goes to the jackpot), and negatively on the variance in the prize distribution (which depends largely on how much goes on smaller prizes). We simulate the effects of envisaged game design changes on sales revenue and find potentially large effects.

The Demand for Lotto: The Role of Conscious Selection

This article presents estimates of the elasticity of demand for lottery tickets using time series data in which there is variation in the expected value of a lottery ticket induced by rollovers. An important feature of our data is that there are far more rollovers than expected given the lottery design. We find strong evidence that individuals do not choose their lottery numbers uniformly from a uniform distribution—that is, conscious selection. We use our estimates to derive the inverse supply function for the industry, and this enables us to identify the demand elasticity. We find the price elasticity to be close to unity, which implies that the operator is revenue maximizing—which is the regulator's objective.

The Demand for Lotto: The Role of Conscious Selection

This article presents estimates of the elasticity of demand for lottery tickets using time series data in which there is variation in the expected value of a lottery ticket induced by rollovers. An important feature of our data is that there are far more rollovers than expected given the lottery design. We find strong evidence that individuals do not choose their lottery numbers uniformly from a uniform distribution—that is, conscious selection. We use our estimates to derive the inverse supply function for the industry, and this enables us to identify the demand elasticity. We find the price elasticity to be close to unity, which implies that the operator is revenue maximizing—which is the regulator's objective.