If information on the effects of the own decision needs to be revealed by the individual, there exists an additional strategy to reduce cognitive dissonance, as they can choose to only reveal information that is congruent with their ideals. This phenomenon is referred to as selective exposure to information (Festinger,
1957). In its simplest form, a person would simply avoid revealing information on the moral implications of their decision to exploit moral wiggle room (Dana et al.,
2007). If the consequences of own decisions for third parties or the environment are unknown, the size of the cognitive dissonance is reduced. In such a case, the individual’s self-image is only challenged by the possibility, not necessarily the fact, that maximizing payoffs corresponds to the less moral option. In our hidden information treatments, it is a priori unclear whether the alternative with the higher monetary payoff is associated with the environmental benefit that is larger (aligned interests) or lower (conflicting interests). Thus, avoiding information and choosing the self-serving option can be a viable alternative to revealing the information and then choosing the greener option even if it is more expensive to do so.
3.1 Individual decision
Consider the binary choice at the basis of our experiment. Denote with \(\omega _B\in \{\underline{\omega }_B,\overline{\omega }_B\}\) the realized amount of offset contribution for Option B and with \(\omega _A\) the certain amount associated with Option A, with \(\underline{\omega }_B<\omega _A<\overline{\omega }_B\). The largest achievable offset contribution d is hence defined by \(d=\textrm{max}\{\omega _A,\omega _B\}\). An individual with green preferences would prefer the option associated with d if her costs c associated with each option were equal (i.e., \(c_B=c_A\)). However, both options differ in costs to the individual, with the self-serving option denoted s for which \(c_s=\textrm{min} \{c_A,c_B\}\).
In the case of individual choices under full information, cognitive dissonance occurs if individuals with (sufficiently intensive) green preferences choose the self-serving product option
s, while
\(\omega _s<\omega _{\lnot s}=d\), i.e., if interests are conflicting. We follow Rabin (
1994) by defining the costs from this dissonance when choosing option
i as a function
\(\Phi (d-\omega _i;\alpha )\), with
\(\Phi (0)=0\),
\(\Phi '>0\),
\(\Phi ''>0\), and parameter
\(\alpha \) representing the intensity of the green preference with
\(\frac{d \Phi }{d\alpha }>0\). Under complete information, and for an endowment
m, the individual’s payoffs for both product options are
$$\begin{aligned} U_s&=m-c_s-\Phi (d-\omega _s), \end{aligned}$$
(1)
$$\begin{aligned} U_{\lnot s}&=m-c_{\lnot s}-\Phi (d-\omega _{\lnot s})= m-c_{\lnot s}. \end{aligned}$$
(2)
Hence, under complete information, the selfish option is strictly dominated iff
$$\begin{aligned} \Phi (d-\omega _s)>\Delta _c=c_{\lnot s}-c_s. \end{aligned}$$
(3)
Thus, for
\(\Delta _c\) small enough, the individual will choose the more expensive product to avoid the cognitive dissonance associated with a self-image as an environmentally conscious individual. However, for larger levels of
\(\Delta _c\), the individual will accept the dissonance with respect to their self-image in favor of their narrow self-interest.
Let us now introduce the possibility of information avoidance as an additional strategy to reduce cognitive dissonance, as in our individual choice treatment with hidden information. For this, we assume the true value of
\(\omega _B\) to be initially unobservable, which implies that it is a priori unclear if interests are aligned or conflicting. Denote with
\(\mu \) the ex ante probability of interests being aligned, i.e.,
\(\mu =P(\omega _s=d)\). Furthermore, we use index
\(k\in \{0,1\}\) to denote the state of the individual’s level of information, with
\(k=1\) representing a situation where the information is revealed, while
\(k=0\) represents non-revelation. Hence, for an uninformed individual
\((k=0)\) for which (
3) holds, the expected costs of cognitive dissonance
\(\Phi _0\) when choosing option
s are determined by the individual’s (subjective) beliefs on the probability of aligned interests as follows:
$$\begin{aligned} \Phi _0=\Phi \left( \hat{E}(d)-\hat{E}(\hat{\omega }_s);\alpha \right) \end{aligned}$$
Notice that even without subjective distortions in beliefs
\(\Phi _0\) is always smaller than under certainty, as represented in (
3), which creates an incentive to simply remain uninformed and choose the self-serving option. This strategy, however, represents a sort of self-deception which, in turn, is likely to be associated with a feeling of displeasure with one’s own self-serving rationalization. To take this into account, we again follow Rabin (
1994) and the subsequent literature by introducing costs of self-deception
\(\Psi (\cdot )\) which increase with the misperception of probability
\(\mu \) and dependent on the amount of available information revealed, i.e., the value of
k. The costs of self-deception for
k signals revealed are
$$\begin{aligned} \Psi _k=\Psi _k \left( (\hat{\mu }_k-\mu _k), k;\beta \right) . \end{aligned}$$
A higher
\(\beta \) represents a greater sensitivity to self-deception, which varies across individuals as well as with contextual variables.
Given these assumptions and for
k signals revealed, the valuation of the self-serving option
s is
$$\begin{aligned} U_k(s)=m-c_s-\Phi _k\left( \hat{E}(d \left| k\right) -\hat{E}(\hat{\omega }_s\left| k\right) \right) -\Psi _k \left( (\hat{\mu }_k-\mu _k), k\right) . \end{aligned}$$
(4)
Note that for the signal revealing the truth with certainty, as assumed here, the case for
\(k=1\) reduces to (
1). Using this setup, we can now proceed to analyze the tendency to avoid information in individual choices under hidden information. To identify the potential for self-serving information avoidance, consider an individual with green preferences (
\(\Phi _0>0\)) for whom, under certainty, (
3) holds, i.e., under certainty they would want to choose the green option, even if it is associated with higher costs
\(c_{\lnot s}\). For simplicity, we assume risk-neutrality. This individual’s expected valuation when planning to reveal the information, but before doing so, is
$$\begin{aligned} EU_{k=1}=m- \left[ \hat{\mu } \cdot c_s+(1-\hat{\mu })\cdot c_{\lnot s} \right] . \end{aligned}$$
(5)
The term subtracted from the endowment
m represents the expected cost before the signal is revealed. In this case, given that (
3) holds, the individual will only choose the self-serving option if interests are aligned; otherwise, option
\(\lnot s\) is purchased. As the individual intends to always choose the “greener” option, no cost from cognitive dissonance will arise.
For such an individual, the decision to remain uninformed is determined by a comparison of (
4) with k=0 and (
5). More precisely, self-serving information avoidance will arise iff
\( U_0(s)> EU_{k=1}\), which is the case for
$$\begin{aligned} \Delta _c>\frac{\Psi _0+\Phi _0}{1-\mu }. \end{aligned}$$
Let us assume, for ease of presentation, that the cognitive dissonance is completely resolved if the voter remains uninformed, i.e.,
\(\Phi _0=0\). Consequently, information will be avoided if, in the uninformed state, the costs of self-deception are not too high compared with the difference in costs. Taking also condition (
3) into account, we can establish a price range, where such information avoidance is self-serving. Information avoidance leads to the exploitation of moral wiggle room iff
$$\begin{aligned} \Phi (d-\omega _s)> \Delta _c>\frac{\Psi _0}{1-\mu }. \end{aligned}$$
(6)
We can thus identify self-serving information avoidance via a comparison of self-serving choices in the full information treatment with those in the treatments where this information can be actively revealed: For a certain range of cost differences, decision-makers would choose the non-selfish option under full information, but remain uninformed and choose selfishly under hidden information. As with increasing differences in costs, condition (
3) is increasingly less likely to hold, we can also expect an increasing share of self-serving choices under full information. Thus, for the parameterization chosen here, we expect information avoidance to be more likely to occur for our lower payoff differences. This is in line with recent experimental evidence on information avoidance in consumption. Momsen and Ohndorf (
2022) report that for information structures with stochastic revelation, self-serving information avoidance is more likely to arise if the differences in payoffs are not too large. A similar effect is reported in Momsen and Ohndorf (
2020) for complete revelation and small but positive information costs.
In order to predict the effects for our voting treatments, we present the situation in our group treatments as a Bayesian voting game with symmetric strategies, as in Feddersen and Pesendorfer (
1997) and Tyson (
2016), where equilibrium strategies are determined via cutoff levels. Notice that our treatments did not allow for abstentions; hence, for the case of complete information, the voter’s choice is determined exclusively via a comparison of expected utilities from voting for options
s and
\(\lnot s\). More precisely, we follow Feddersen and Pesendorfer (
1997) and Tyson (
2016) by determining the cutoff levels in the (subjective or objective) distribution of voter preferences at which a specific voter would switch from voting for option
\(\lnot s\) to option
s .
To represent our voting treatments, let there be
\(n + 1\) voters indexed by
\(j\in \{1,\ldots , n + 1\}\). As decisions are not only taken for the individual, but for the whole group, we introduce an additional utility component, denoted by
\(\nu _j\), which arises if the green option is chosen for the whole group. Thus, in contrast to the considerations by Brennan and Lomasky (
1993), an individual choice framed as a consumption decision might not be considered an appropriate baseline treatment. We therefore included the dictatorship treatment to provide an additional point of comparison with our voting treatments.
As we are interested in moral biases, our analysis focuses exclusively on situations with conflicting interests, which is also standard when considering moral wiggle room (Dana et al.,
2007). Thus, in this case, situation
\(\lnot s\) will be the greener option. The option that is chosen for the whole group is determined via simple majority voting. Thus, if the number of votes for option
s is larger or equal to
\((n/2+1)\), option
s will be the outcome for all voters, otherwise
\(\lnot s\) will be chosen. Again, note that abstentions are impossible here, such that voter
j’s strategy space is simply
\(S=\{\lnot s_j; s_j\}\), i.e., the only decision to be made is whether to vote for one option or the other.
We denote with
\(\pi _t\) the (subjective) probability of the individual being pivotal, and with
\(\pi _s\) (
\(\pi _{\lnot s}\)) the (subjective) probability of the low (high) cost option being chosen if the player is not pivotal. In a conflicting interest situation under full information, voter
j’s expected payoff when casting a vote for option
\(\lnot s\) is
$$\begin{aligned} U_{\lnot s}^v=m+\pi _t \left( \nu _j-c_{\lnot s}\right) +\pi _{\lnot s} \left( \nu _j-c_{\lnot s}\right) -\pi _s c_s, \end{aligned}$$
(7)
while voting for option
s yields
$$\begin{aligned} U_{ s}^v=m-\pi _t c_s+ \pi _{\lnot s} \left( \nu _j-c_{\lnot s}\right) -\pi _s c_s-\Phi ^v_j \end{aligned}$$
(8)
Notice here that the additional utility component
\(\nu _j\) always arises if the group decision is in favor of option
\(\lnot s\) independently of whether the vote of individual
j is decisive. Hence,
\(\nu _j\) is not interpreted as some sort of imperfect altruism, but represents a form of instrumental utility from choosing the greener option. Note that the total amount of contributions to offsets will increase with group size, as choosing
\(\lnot s\) will increase the contribution to the offset for every individual in the group. Hence, as pointed out by Aldrich (
1993) and Myatt (
2015), the decrease in expected instrumental utility with increasing
n is likely to be lower than that modeled in Brennan and Lomasky (
1993). Note that this effect would strengthen the prediction made by the low-cost theory of voting that larger
n would increase the likelihood of more moral outcomes, as not only the relative weight of the expressive utility component increases with
n, but also instrumental utility might change in favor of the greener option
\(\lnot s\).
Note also that, within (
7) and (
8), we continue to assume
\(\Phi ^v_j=\Phi (d_j-\omega _i;\alpha _j, n)\) to be the costs of dissonance, with
\(\Phi (0)=0\),
\(\Phi '>0\),
\(\Phi ''>0\), and
\(d_j\in \{\omega _s; \omega _{\lnot s}\}\). Parameter
\(\alpha \) represents the intensity of the green preference, with
\(\frac{d \Phi }{d\alpha }>0\). We further assume that
\(\alpha \in [0, \bar{\alpha }]\) is distributed over the voter population with probability distribution
\(F_\alpha \). The single voter knows their own preference level and the distribution
F over the entire population.
Following Feddersen and Pesendorfer (
1997), we denote a pure strategy for voter
j as
\(\rho _j\), which is a measurable function from her preference type
\(\alpha \) to a vote choice, i.e.,
\(\rho _j : \mathbb {R} \rightarrow S \) and a mixed strategy
\(\bar{\rho }_j\) is a measurable function from a voter’s type
\(\alpha \) to the probability of voting for option
s, i.e.,
\(\bar{\rho }_j : \mathbb {R} \rightarrow [0,1] \).
Let us denote with
\(\hat{\alpha }\) the cutoff preference level for which
\(U_{\lnot s}^v=U_{ s}^v \) [as in (
7) and (
8)], i.e.,
$$\begin{aligned} \Phi ^v(\hat{\alpha })=\pi _t \ (\Delta _c- \nu ). \end{aligned}$$
(9)
Thus,
\(\hat{\alpha }\) represents the preference type that is indifferent between choosing
s and
\(\lnot s\). As under full information this is the only choice to be made, the formulation of the voter’s strategy is almost trivial. Depending on their preference type
\(\alpha \), the voter will choose the option that maximizes their utility. Hence, as abstentions are impossible, the voter’s dominant strategy for any
\(\hat{\alpha }\) is
$$\begin{aligned} \bar{\rho }_j(\alpha _j)={\left\{ \begin{array}{ll}1 \text { for } \alpha _j<\hat{\alpha } \\ 0 \text { for } \alpha _j>\hat{\alpha }\\ \frac{1}{2} \text { for } \alpha _j=\hat{\alpha } \end{array}\right. } \end{aligned}$$
(10)
Thus, for any distribution
f over
\(\alpha \) (or a belief thereof), the probability
q that a randomly selected voter votes for
s under complete information is
$$\begin{aligned} q^{f} = \int _0^{\hat{\alpha }} \bar{\rho }_j(\alpha _j) \ f(\alpha ) \ \textrm{d} \alpha \end{aligned}$$
(11)
In other words,
\(q^{f}\) is the probability that any randomly drawn voter will choose the selfish option
s. Hence, for the corresponding unique symmetric Nash equilibrium
\(\bar{\rho }^*\), the probability of being pivotal in our voting treatments is determined by the standard binomial distribution
$$\begin{aligned} \pi _t(q)=\left( {\begin{array}{c}n\\ n/2\end{array}}\right) \cdot q^{\frac{n}{2}}\cdot (1-q)^{\frac{n}{2}} \end{aligned}$$
(12)
where we substitute
\(q=q^{f}\).
Notice that for our Voting3 and Voting11 treatments, the initial expectations over
q might differ among subjects, as they might have different beliefs over the distribution
\(f(\alpha )\). Yet, we can expect the following considerations to hold for aggregated decisions. Note further that for our Dictator treatment, the dominant strategy would also be determined by (
9) and (
10), while pivotality
\(\pi _t\) is fixed exogenously at 1/3. Thus, for all group treatments, it follows from (
9) and (
10) that a subject in a situation with conflicting interests will choose the greener option
\(\lnot s\) with certainty if and only if
$$\begin{aligned} \nu +\frac{\Phi ^v(\alpha _j)}{\pi _t}>\Delta _c, \end{aligned}$$
(13)
i.e., if the costs of cognitive dissonance divided by the probability of being pivotal and the additional utility if the green option is implemented for the entire group exceed the difference in costs between the selfish and the non-selfish option.
Several interesting observations can be made with respect to this result. First, notice that this condition is relaxed with a decrease in the probability of being pivotal \(\pi _t\). Thus, with decreasing probability of the own vote being decisive, voting for option \(\lnot s\) is more likely to be used as a strategy to avoid cognitive dissonance (cost \(\Phi ^v\)). If it is unlikely that voting for the “greener” option will affect the outcome, players can hence use the vote to align their choice with their own environmental ideals. The vote will thus reflect what the individual considers to be morally preferable, rather than being guided by their own narrow self-interest. This corresponds to the result derived from theories of expressive voting, where “moral” votes are likely to increase with larger constituencies. Thus, we formulate the following hypothesis:
Notice that for n=10, which corresponds to our Voting11 treatment, the largest possible pivotality that can be derived from (
12) is
\(\pi _t=0.25\), which would be the case for
\(q=1/2\). Hence, there exists no distribution of voter preferences
q for which the probability of being pivotal
\(\pi _t\) is larger than 1/4.
16 Consequently, for rational beliefs over
q, the pivotality in Voting11 will always be smaller than for the Dictator treatment, which is exogenously set to 1/3. Thus, from (
13), we formulate the following hypothesis for a comparison of behavior in a group with majority voting relative to a randomized dictatorship in situations with conflicting interests:
Next, we consider voting decisions if players have the possibility to avoid information, as in our voting treatments with hidden information. In this case, we also consider the subjective probabilities for the outcome in the uninformed state. Thus, denote with \(\pi _{t}^{u}\) the uninformed individual’s subjective probability of being pivotal, and with \(\pi _{s}^{u}\) (\(\pi _{\lnot s}^{u}\)), the subjective probability of a majority for the low (high) cost option if the uninformed player is not pivotal. While these probabilities might be subject to individual over- or underestimation, we assume sufficient rationality in the sense that subjective probabilities add up to 1, i.e., \(\pi _{s}^{u}+\pi _{\lnot s}^u+\pi _{t}^{u}=1\).
For ease of presentation, we again assume that the cognitive dissonance is completely resolved if the voter remains uninformed, i.e.,
\(\Phi _0^v=0\), and only costs of self-deception
\(\Psi _0^v\) arise. Thus, analogous to (
5) in the individual case, the voter’s expected payoff if information is avoided is as follows:
$$\begin{aligned} U_{k=0}^h(s)=m-\left( \pi _{\lnot s}^u c_{\lnot s}+ \pi _{s}^{u} c_s+\pi _{t}^{u} c_{s}\right) -\Psi _0^v(\beta ,k) \end{aligned}$$
(14)
In order to establish a cutoff preference level
\(\hat{\beta }\) separating informed and uninformed voters, this payoff needs to be compared with the ex ante expected payoff of a voter deciding to reveal information. Note that a voter with
\(\alpha <\hat{\alpha }\) would always choose the option
s, as established above. As interests are aligned with probability
\(\mu \), an informed voter with
\(\alpha >\hat{\alpha }\) would vote for option
\(\lnot s\) in case of conflicting interests, i.e., her expected payoff before revealing information is
$$\begin{aligned} EU_{k=1}^h= m- \mu c_s - (1-\mu ) \left[ \pi _t \left( -\nu +c_{\lnot s}\right) +\pi _{\lnot s} \left( -\nu +c_{\lnot s}\right) +\pi _s c_s\right] . \end{aligned}$$
(15)
Thus, there potentially exist two different cutoff levels for preference parameters
\(\alpha \) and
\(\beta \), which are distributed with distribution function
\(F(\alpha , \beta )\).
We define the cutoff preference level
\(\hat{\beta }\) as the value of
\(\beta \) for which
\(U_{k=0}^v(s)= EU_{k=1}^v\), i.e., the preference level for which an individual is indifferent between revelation and non-revelation of information. For ease of presentation, we assume that at the margin, the voter will vote for the self-serving option
s. In this case, and for
\(\hat{\alpha }\) as determined in (
9), the dominant strategy for any voter is
$$\begin{aligned} \bar{\rho }_j(\alpha _j, \beta _j)={\left\{ \begin{array}{ll}1 \text { for } \beta _j \le \hat{\beta } \\ 1 \text { for } \beta _j>\hat{\beta } \text { and } \alpha _j \le \hat{\alpha }\\ 0 \text { for } \beta _j>\hat{\beta } \text { and } \alpha _j>\hat{\alpha } \end{array}\right. } \end{aligned}$$
(16)
The probability of any individual choosing the selfish option in any type of situation is then
$$\begin{aligned} q^{H} = F_{\alpha }(\hat{\alpha })\ \bar{\rho }(\alpha ) + F_{\beta } (\hat{\beta })\ \bar{\rho }(\beta ) - \int _0^{\hat{\alpha }}\int _0^{\hat{\beta }} \bar{\rho }(\alpha , \beta , k)\ f(\alpha ,\beta ) \ \textrm{d} \alpha \ \textrm{d} \beta \end{aligned}$$
(17)
Note that for a situation with aligned interests, both informed and uninformed voters would choose option
s. Thus, an uninformed voter who observes
\(\lnot s\) being chosen can infer that
\(\lnot s\) must be the “greener” option (i.e., the situation features a conflict of interests), as it generated a positive number of votes. Thus, we can reformulate (
14) as follows
$$\begin{aligned} U_{k=0}^h(s)=m- \mu c_s - (1-\mu ) \left( \pi _{\lnot s} (c_{\lnot s}-\nu ) + \pi _{s} c_s+\pi _{t} c_{s}\right) -\Psi _0^v \end{aligned}$$
(18)
The cutoff level
\(\hat{\beta }\) is hence determined via equality of (
15) and (
18), which leads to the following implicit definition:
$$\begin{aligned} \psi (\hat{\beta }) = (1-\mu ) \pi _t(q^h) \left( \Delta _c-\nu \right) \end{aligned}$$
(19)
Note that, again,
\(\pi _t(q^h)\) is determined analogously to the full information case via substitution of (
17) in (
12) for our voting treatments, while it is exogenously set to 1/3 in our Dictator treatment.
Exploitation of moral wiggle room via information avoidance arises if voters remain uninformed and vote for the self-serving option
s who would have chosen
\(\lnot s\) under full information. As information costs are zero, we can thus, using (
13), (
16), and (
19), establish the following condition for which a voter
j exploits moral wiggle room via self-serving information avoidance:
$$\begin{aligned} \nu +\frac{\Phi ^v(\alpha _j)}{\pi _t(q^f)}>\Delta _c>\nu +\frac{\Psi _0^v(\beta _j)}{(1-\mu ) \ \pi _t(q^h)}. \end{aligned}$$
(20)
This result is particularly interesting. If (
20) holds, expressive voting is no longer the voter’s preferred strategy to resolve the internal conflict between self-interest and environmental ideals. Instead, the player’s corresponding cognitive dissonance is managed via the avoidance of information on the effects of their own choice. These subjects with green preferences of intermediate intensity will remain uninformed and choose the self-serving option, even if their choice had been the opposite under full information.
As shown in the mathematical appendix, for an increasing number of voters
n, the left-hand side in (
20) increases at a higher pace than the right-hand side. This implies that if a constituency becomes larger, the range of payoffs for which information avoidance is the dominant strategy increases. Hence, while we expect a larger number of “green” choices in the Voting11 treatment under full information than in the corresponding Voting3 treatment due to expressive voting, this difference should be significantly lower for the respective treatments with hidden information. In other words, it can be expected that a larger share of voters will substitute expressive voting with information avoidance in Voting11 than in Voting3, as it is the dominant strategy.
Furthermore, the upper boundary of (
20) is more likely to be exceeded for our larger price differences. Hence, again, self-serving information avoidance can be expected to be more likely to occur for our lower price differences. We summarize these predictions in the following hypothesis:
As laid out above, for rational beliefs, the largest possible pivotality in our Voting11 treatment is \(\pi _t=1/4<1/3\). In the mathematical appendix, we show that if beliefs are rational (or at least the formation thereof), the above-made considerations also hold for the comparison of our Voting11 and Dictator treatments. We can hence formulate an analogous hypothesis: