It has been shown that a gamble is judged to be more attractive when its zero outcome is designated as “losing $0” rather than “winning $0,” an instance of what we refer to as the mutable-zero effect

The framing of nothing and the psychology of choice. Marc Scholten, Daniel Read, Neil Stewart. Journal of Risk and Uncertainty, December 3 2019. https://link.springer.com/article/10.1007/s11166-019-09313-5

Abstract: Zero outcomes are inconsequential in most models of choice. However, when disclosing zero outcomes they must be designated. It has been shown that a gamble is judged to be more attractive when its zero outcome is designated as “losing $0” rather than “winning $0,” an instance of what we refer to as the mutable-zero effect. Drawing on norm theory, we argue that “losing $0” or “paying $0” evokes counterfactual losses, with which the zero outcome compares favorably (a good zero), and thus acquires positive value, whereas “winning $0” or “receiving $0” evokes counterfactual gains, with which the zero outcome compares unfavorably (a bad zero), and thus acquires negative value. Moreover, we propose that the acquired value of zero outcomes operates just as the intrinsic value of nonzero outcomes in the course of decision making. We derive testable implications from prospect theory for mutable-zero effects in risky choice, and from the double-entry mental accounting model for mutable-zero effects in intertemporal choice. The testable implications are consistently confirmed. We conclude that prevalent theories of choice can explain how decisions are influenced by mutable zeroes, on the shared understanding that nothing can have value, just like everything else.

Keywords: Descriptive invariance Norm theory Counterfactuals Zero outcomes Risk and time Prospect theory Double-entry mental accounting model
JEL Classifications: D00 D90 D91



4 General discussion
The valence of a zero event depends on its “irrelevant” description: It “feels better” to
lose or pay nothing than to win or receive nothing. A negative wording (lose, pay) sets
up a norm of negative events, with which the zero event compares favorably, while a
positive wording (win, receive) sets up a norm of positive events, with which the zero
event compares unfavorably, so that a negative wording acquires a more positive tone
than a positive wording. Descriptive invariance requires from us that this should not
affect our decisions, but we have shown that it does, among a fair number of us at least.
To others among us, the framing of zero events may actually be irrelevant. The
mutable-zero effect is indeed small; yet, it is a reliable phenomenon. And if one thinks
of the alternative descriptions of a zero outcome as a minimal manipulation, the small
effect may actually be considered quite impressive (Prentice and Miller 1992).
Descriptive invariance, along with dominance, is an essential condition of rational
choice (Tversky and Kahneman 1986), and it has seen a number of violations,
commonly referred to as framing effects. A stylized example of framing is the adage
that optimists see a glass of wine as half full, while pessimists see it as half empty. And
if the wine glass is half full, and therefore half empty, then these are complementary
descriptions of the same state of the world, so that, normatively, using one or the other
should not matter for judgment and choice (Mandel 2001)—but it does.

4.1 Counterfactuals versus expectations
Life often confronts us with zero events. A bookstore may offer us “free shipping.” Our
employermay grant us “no bonus.”We are pleased to pay $0 to the bookstore, and this may be
because we expected to pay something but did not.We are not pleased to receive $0 from our
employer, and this may be because we expected to receive something but did not (Rick and
Loewenstein 2008). In norm theory, Kahneman and Miller (1986) suggested that reasoning
may not only flow forward, “from anticipation and hypothesis to confirmation or revision,” but
also backward, “from the experience to what it reminds us of or makes us think about” (p.
137). In the latter case, “objects or events generate their own norms by retrieval of similar
experiences stored in memory or by construction of counterfactual alternatives” (p. 136). Thus,
“free shipping” may sound pleasant because it reminds us of occasions on which we were
charged shipping fees, and “no bonus” may sound unpleasant because it reminds us of
occasions on which we were granted bonuses; not so much because we expected to pay or
receive something. Of course, both norms and expectations may influence our feelings, and
may be difficult to disentangle in many real-life situations. Kahneman and Miller’s (1986)
intention with norm theory was “not to deny the existence of anticipation and expectation but
to encourage the consideration of alternative accounts for some of the observations that are
routinely explained in terms of forward processing” (p. 137, emphasis added). Our intention
was to compile a set of observations that cannot reasonably be explained in terms of forward
processing, which therefore constitute the clearest exposure of norms.

4.2 Expectations in decision theory
We have incorporated counterfactuals into theories of choice, so as to predict the effects
of mutable zeroes when people face risk and when people face time. Traditionally,
decision theory has ignored counterfactuals, but expectations play a role in most
theories of decision under risk. While prospect theory sacrifices the expectation
principle from EU, by assigning a decision weight w(p) to probability p of an outcome
occurring, other formulations have maintained the expectation principle but modified
the utility function. For instance, the utility function has been expanded with anticipated
regret and rejoicing as they result from comparisons between the possible outcomes
of a gamble and those that would occur if one were to choose differently (Bell 1982,
1983; Loomes and Sugden 1982). Similarly, the utility function has been expanded
with anticipated emotions as they result from comparisons between the possible
outcomes of a gamble with the expected value of the gamble: Anticipated disappointment
when “it could come out better,” and anticipated elation when “it could come out
worse” (Bell 1985; Loomes and Sugden 1986). Zero outcomes acquire value in the
same way as nonzero outcomes do: Either from between-gamble or within-gamble
comparisons. Thus, a zero outcome acquires negative value (by regret or disappointment)
if the comparison is with a gain, and positive value (by rejoicing or elation) if the
comparison is with a loss. In our analysis, however, zero outcomes are unique, in that
only they elicit counterfactual gains and losses, which will then serve as a reference
point for evaluating the zero outcomes themselves. Nonetheless, in Experiment 3,
dealing with zero outcomes in intertemporal choice, we obtained a result suggesting
that between-prospect comparisons of zero and nonzero outcomes also affected choice.

4.3 The framing of something, the framing of nothing
The investigation of framing effects in judgment and decision making began with
Tversky and Kahneman’s (1981) Asian Disease Problem, in which the lives of 600
people are threatened, and life-saving programs are examined. One group of participants
preferred a program that would save 200 people for sure over a program that
would save 600 people with a 1/3 probability, but save no people with a 2/3 probability.
Another group of participants preferred a program that would let nobody die with a
probability of 1/3, but let 600 people die with a 2/3 probability, over a program that
would let 400 people die for sure. Prospect theory ascribes this result to reference
dependence, i.e., v(0) = 0, and diminishing sensitivity, i.e., v is concave over gains, so
that v(600) < 3v(200), which works against the gamble, and convex over losses, so that
v(−600) > 3v(−200), which works in favor of the gamble.
Our interpretation is that some of the action may lie in the zero outcomes, rather than
the nonzero outcomes. Specifically, “save no people” brings to mind saving some
people, with which saving no people compares unfavorably, thus working against the
gamble. Similarly, “let nobody die” brings to mind letting somebody die, with which
letting nobody die compares favorably, thus working in favor of the gamble. Reference
dependence is fine, but designating zero outcomes means that v(0) ≠ 0, because the
reference point is no longer the status quo, but rather something imagined.
There is no shortage of competing views on framing effects (for one of many
discussions, see Mandel 2014), and our norm-theory approach to the Asian Disease
Problem is a partial explanation at best. Indeed, the reversal from an ample majority
(72%) choosing the safe option in the positive frame (saving lives) to an ample majority
(78%) choosing the risky option in the negative frame (giving up lives) is a large effect,
whereas the mutable-zero effect is a small effect, unlikely to be the sole responsible for
Tversky and Kahneman’s (1981) result. However, judgments and decisions are influenced
by the framing of zero outcomes, and we have shown that prevalent theories of
choice, Kahneman and Tversky’s (1979) prospect theory and Prelec and Loewenstein’s
(1998) double-entry mental accounting model, can explain how decisions are influenced
by mutable zeroes, on the shared understanding that nothing can have value, just
like everything else.