Prospect Theory: Lotteries that Save Money

Clement Wong


May 27th, 2012

An outline and analysis of PLS: Prize-Linked Savings, and the behavioural economics of lotteries in general.

Every now and then, the media makes a big deal out of winning the lottery. When the prize pool billows into something incredible, attention is turned to who the next multi-millionaire will be. Do these stories make you dream of living a life in the lap of luxury?Many see lotteries as a chance to score their big break, and as a result invest regularly in tickets. Seeking to lean on our appetite for what some bluntly call a ‘tax on stupidity’, Prize-Linked Savings is a program that attempts to do economic good rather than harm.

Prize-Linked Savings (PLS) is an atypical service some overseas banks and credit unions offer. Interest generated in lottery-linked deposit accounts (LLDAs) are, as the name suggests, partially collated to fund lottery prize pools. The appeal comes from providing a more exciting incentive to save – a chance to win huge sums of cash. Attaching fervor to saving should in turn, increase the household saving rate and promote financial prudence, particularly in low-income families. The program isn’t without its drawbacks however. With a lottery based system, random and inequitable distribution of interest generated on savings is a given. Additionally, the opportunity cost here will be significant – with payoffs of the lottery racking up well into the thousands, participants are foregoing higher regular interest payments. As a collective, these people would be better off with a traditional banking account. What is it about lotteries that make the PLS program so eagerly received in some parts of Africa, Asia, Europe, and America?

First, a short primer on an important behavioural economics framework. Tversky and Kahneman’s seminal paper on prospect theory[1] in particular, will later highlight the possible forces at play. Their work indicated that utility functions of individuals exhibited a few interesting characteristics. Firstly, static levels of wealth were not as important as the changes in wealth; that net outcomes and movements from an individual’s reference point were the determinants of utility. Loss aversion suggested that negative net outcomes were much more impactful in loss of utility when compared against the magnitude of utility in net gains. In both directions, utility would incur diminishing marginal returns, suggesting insensitivity as the net change increases in a given direction. These are shown in the diagram adjacent. One other important observation beyond the scope of the diagram was that individuals placed unfairly heavy weights upon improbable outcomes. People were poor assessors of the true odds of an event occurring as it became more and more unlikely.

Extending prospect theory to PLS now surfaces the reasons behind its success. While typical lotteries involve outlays to purchase tickets – an incurrence of loss (point A in the diagram above)[2], participation in PLS lotteries are perceived differently. As the funding comes from foregoing some interest earned in their LLDAs, participation in the lottery is seen as a reduction in net gains (point C as compared against point B). A reduced gain is still viewed favourably, as the net outcome is ultimately positive. Additionally, the inability to accurately judge probabilities in winning lotteries will suggest that individuals will be overly optimistic, overestimating their chances of striking it rich. Unaware of their misconceptions, people will regard PLS as more than it really is.

That is not to say that Prize-Linked Savings is an inherently bad program. Certain countries like the United States, the United Kingdom and South Africa amongst others have mediocre household saving rates, which could be improved upon. While usually a reflection of the interest rates on offer, there is an external motive to promote a stronger household saving rate. The practical implication of a low saving rate is that few low-income households have enough funds to survive an emergency or unavoidable expense – many individuals are financially fragile[3]. Here in Australia, the need may not be quite so apparent. Household saving rates were low over the 2000’s, but have picked up sharply following the global financial crisis[4]. That said, there will certainly be families in every country that could benefit from the tantalizing, if over-optimistic incentives of PLS. Even if they fail to win any lotteries, their access to funds will improve through saving over time.

Prize-linked savings is a novel idea, as well as a double edged sword. While its goals are admirable in promoting savings which in turn encourages financial responsibility, its lottery mechanisms are intrinsically inefficient. Prospect theory tells us that individuals are inclined to see these lotteries favourably, oblivious to the truly poor odds. Ideally participants will eventually learn the inherent benefits of prudence, and substitute into more traditional and efficient banking accounts as their starry eyed day dreaming becomes grounded in reality. Prize-linked savings should be promoted as a transitional measure, an ingeniously structured stepping stone for those who have yet to see the benefits in saving.

[1] Amos Tversky, Daniel Kahneman, “Judgement under Uncertainty: Heuristics and Biases”, Science 185 (1974): 1124-31

[2] Lottery participation may become habitual in some individuals, where ticket purchases are considered the status quo – a net outcome of no change. At this point, invested individuals may no longer see participation as a utility loss.


[4] “Changing Patterns in Household Saving and Spending,” Philip Lowe, Reserve Bank of Australia, September 22, 2011,

The views expressed within this article are those of the author and do not represent the views of the ESSA Committee or the Society's sponsors. Use of any content from this article should clearly attribute the work to the author and not to ESSA or its sponsors.

  • Lolimar

    That’s a pretty cool idea actually – cool being interesting, without being subjective about it.

    But just wondering, has there been any research or examples of what happens if you reduce the variability of the lottery? That is, make it more likely you’ll win, but just not win as much?

    Or maybe you could engineer the expected value of the lottery to be the same as the interest rate you would normally get. That way in the LR, you would not be forgoing any interest, but you would still get the adrenaline boosts from big wins?

    • Clement Wong

      The lottery payouts do vary from the hundreds to well into the thousands – not sure how much the odds change in tandem, but there should be a spectrum.

      I would think it’s possible to create lotteries that have the same expected value of regular interest payments, but from my perspective it’s an unconvincing long-term solution. Assuming that the main demographic PLS appeals to are lower income, low-savings households, a greater proportion of their consumption is relatively inflexible. Their consumption should benefit more from regular and sustainable interest rather than sudden shocks that cannot be expected to reoccur with the same consistency.

      That said, perhaps I’m too heavily discounting the ecstasy of winning a lottery.

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