The prospect of a perfect ending: Loss aversion and the round-number bias

Abstract

Studies across a range of domains have shown that individuals tend to focus on round numbers as cognitive reference points; a so-called left-digit effect. We explain this effect by combining analog numerical heuristics with prospect theory in order to develop an analog value function that predicts the key characteristics of the left-digit effect. Most importantly, this value function predicts an unreported phenomenon, namely; that the left-digit effect will be more pronounced in situations involving losses (cf. gains). We confirm this prediction in both a laboratory experiment regarding hypothetical investments and analysis of buy-sell imbalances in over 15 million trades by investors in a financial market. We conclude that our analog value function is a promising explanation for the left-digit effect. Furthermore, we suggest that interventions aimed at reducing costly buy-sell imbalances in financial markets should focus on the decisions made by investors when they are facing loss. IntroductionResearch has revealed that small changes in prices can significantly influence individuals' perceptions of an item's cost. The left-digit effect (LDE) or "pricing in the nines" (Basu, 1997;Stiving, 2000) occurs when two prices that differ by 1 cent (e.g., $2.99 vs. $3.00) are encoded differently in the perceiver's mind due to differences in their left digits. This has clear applications in the pricing of commercial goods and services (Manning & Sprott, 2009;Stiving, 2000; Thomas & Morwitz, 2005). However, recent studies suggest that the LDE could play a role in a broad range of decision-making domains (e.g., in financial markets, see Bhattacharya, Holden, & Jacobsen, 2012). In light of the importance of this phenomenon, we develop a theory to explain the observed LDE. In particular, we combine dual-process theories of numerical processing during the encoding of price information (Gordon, 2004;Lemer, Dehance, Spelke, & Cohen, 2003) and prospect theory's value function (Kahneman & Tversky, 1979; Tversky & Kahneman, 1992) to develop a new analog value function.The analog value function is based on two ideas: (1) individuals may use changes in leftdigits to inform their judgment of changes in value; and (2) changes in left-digits will bias choices more readily in situations involving losses than in situations involving gains. Under the dual-process paradigm, the use of simple left-digit heuristics implies a reliance on intuitive type 1 processing rather than the more deliberative type 2 processing associated with calculating the precise change in value (Evans & Stanovich, 2013a, Hogarth, 2001 Kahneman & Frederick, 2002;Payne, Bettman, & Johnson, 1993;Sloman, 1996;Stanovich & West, 2000). However, our theory is not based on the premise that there must be a change in reasoning strategy from more normative in the context of gains to heuristic in the context of losses. Rather, we consider prospect theory and propose that the salience of left-digit changes may be exaggerated by loss aversion. The higher salience of l...

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