Objective numeracy exacerbates framing effects from decision-making under political risk

While Prospect Theory helps to explain decision-making under risk, studies often base frames on hypothetical events and fail to acknowledge that many individuals lack the ability and motivation to engage in complex thinking. We use an original survey of US adults (N = 2813) to test Prospect Theory in the context of the May 2023 debt ceiling negotiations in the US Congress and assess whether objective numeracy moderates framing effects. We hypothesize and find evidence to suggest that most respondents are risk-averse to potential gains and risk-accepting to potential losses; however, high numerates are more risk-averse and risk-accepting to gains and losses, respectively, than low numerates. We also find that need for cognition interacts with numeracy to moderate framing effects for prospective losses, such that higher need for cognition attenuates risk-acceptance among low numerates and exacerbates risk-acceptance among high numerates. Our results are robust to a range of other covariates and in models accounting for the interaction between political knowledge and need for cognition, indicating joint moderating effects from two knowledge domains similarly conditioned by the desire to engage in effortful thinking. Our findings demonstrate that those who can understand and use objective information may remain subjectively persuaded by certain policy frames.

As you know, the U.S. government has reached its debt limit and is at risk of defaulting on its debt as of June 5, 2023.The White House and GOP negotiators have reached a compromise to raise the debt ceiling and avoid default, but Congress has yet to vote on this deal and the economic impact remains unknown.Imagine that raising the debt ceiling is expected to affect 6 million jobs and you are tasked with deciding between two alternative deals.Which would you choose?
[Jobs Gained Frame] If Deal A is chosen, 2 million jobs will be preserved; If Deal B is chosen, there is a 1 3 probability that 6 million jobs will be preserved and 2 3 probability that no jobs will be preserved.
[Jobs Lost Frame] If Deal A is chosen, 4 million jobs will be lost; If Deal B is chosen, there is a 1 3 probability that no jobs will be lost and 1 3 probability that 6 million jobs will be lost.
We created a dummy variable for each set of responses, coded according to the expected modal response in Prospect Theory: For the Jobs Gained Frame, the dummy variable indicates whether respondents chose the 'sure thing' Deal A or the 'risky' Deal B (coded 1 and 0, respectively).For the Jobs Lost Frame, the dummy variable indicates whether respondents chose the 'sure thing' Deal A or the 'risky' Deal B (coded 0 and 1, respectively).
Numeracy .We assessed respondents' ability to understand and use numeric information using an 11-item objective numeracy scale 2 : Imagine that we rolled a fair, six-sided die 1,000 times.Out of 1,000 rolls, how many times do you think the die would come up even (2, 4, or 6 )?
In the BIG BUCKS LOTTERY, the chances of winning a $10.00 prize are 1%.What is your best guess about how many people would win a $10.00 prize if 1,000 people each buy a single ticket from BIG BUCKS?
In the ACME PUBLISHING SWEEPSTAKE, the chance of winning a car is 1 in 1,000.What percent of tickets of ACME PUBLISHING SWEEPSTAKES win a car?Which of the following numbers represents the biggest risk of getting a disease? 1 in 100, 1 in 1000, 1 in 10.
Which of the following represents the biggest risk of getting a disease?1%, 10%, 5%.If the chance of getting a disease is 10%, how many people would be expected to get the disease out of 100?
If the chance of getting a disease is 10%, how many people would be expected to get the disease out of 1000?
If the chance of getting a disease is 20 out of 100, this would be the same thing as having a % chance of getting the disease.
The chance of getting a viral infection is .0005.Out of 10,000 people, about how many of them are expected to get infected?
We first created a dummy variable for each question to indicate whether respondents provided the incorrect or correct response for each question (coded 0 and 1, respectively).
We also coded all non-responses as zero and note that tests wherein we excluded these responses did not substantively change our results.We then combined responses into an additive index (α = 0.80) such that higher values indicate higher objective numeracy.Finally, as is common in other numeracy literature 3,4 , we created a binary measure of objective numeracy, based on a median split of the additive index, to indicate low and high objective Numeracy (coded 0 and 1, respectively).
Authoritarianism.We assessed respondents' level of authoritarianism, i.e., "a personality adaptation that values social cohesion and conformity to ingroup norms over personal freedom and individual autonomy," 5 (540) using a battery of questions that tasks respondents with choosing between pairs of desirable qualities in children: Although there are a number of qualities that people feel that children should have, every person thinks that some are more important than others.Below are pairs of desirable qualities.For each pair, please indicate which one you think is more important for a child to have.Independence or respect for elders, Curiosity or good manners, Obedience or self-reliance, Being considerate or well-behaved.
We coded responses for respect for elders, good manners, obedience, and well behaved as 1 and responses for independence, curiosity, self-reliance, and being considerate as 0. We combined these responses into a single measure (α = 0.59) and recoded it to range from 0 to 1, such that higher values represent higher Authoritarianism.
Party Identification.We assessed respondents' partisan identity with a combination of two questions: Ideology .We assessed respondents' self-reported ideology with the following question: cific issue of the national debt limit and in politics more generally, with a series of three questions: How closely are you following the debate over the national debt limit?Extremely We reverse coded responses to all three questions, combined these items into averaged scale (α = 0.87), and recoded the measure to range from 0 to 1, such that higher values represent greater Political Interest.
Political Trust.We assessed respondents' level of political trust 19 with the following question: How often can you trust the federal government in Washington to do what is right?Always, Most of the time, About half the time, Some of the time, Never.We recoded responses to range from 0 to 1.
Need for Closure.We assessed respondents' need for closure, i.e., "the expedient desire for any firm belief on a given topic, as opposed to confusion and uncertainty," 10,11 (348) with the following 15-item battery, which asked respondents to indicate (on a sevenpoint scale ranging from Strongly disagree to Strongly agree) how much they disagree or agree with the following statements: 1) I don't like situations that are uncertain; 2) I dislike questions which could be answered in many different ways; 3) I find that a wellordered life with regular hours suits my temperament; 4) I feel uncomfortable when I don't understand the reason why an event occurred in my life; 5) I feel irritated when one per- We averaged together all responses (α = 0.85) and recoded the measure to range from 0 to 1, such that higher values represent greater Need for Closure.
Need for Cognition.We assessed the need for cognition, i.e., "a stable personality trait that describes individuals' tendency to engage in and enjoy effortful cognitive activity," 12,13 (1870) using the six-item, NCS-6 scale, which asked respondents to indicate (on a six-point scale ranging from Strongly agree to Strongly disagree) how much they agree or disagree with the following statements: 1) I would prefer complex to simple problems; 2) I like to have the responsibility of handling a situation that requires a lot of thinking; 3) Thinking is not my idea of fun; 4) I would rather do something that requires little thought than something that is sure to challenge by thinking abilities; 5) I really enjoy a task that involves coming up with new solutions to problems; and 6) I would prefer a task that is intellectual, difficult, and important to one that is somewhat important but does not require much thought.
We reverse coded all items, combined all items into an averaged scale (α = 0.72), and recoded the measure to range from 0 to 1, such that higher values represent greater Need for Cognition.
Big Five Personality Traits.We assessed respondents' Big Five personality traits 14 with a battery that asked to indicate (on a seven-point scale ranging from Disagree strongly to Agree strongly) the following: Here are a number of personality traits that may or may not apply to you.Please indicate the extent to which you agree or disagree with each statement.You should rate the extent to which the pair of traits applies to you, even if one characteristic applies more strongly than the other: 1) Extraverted, enthusiastic; 2) Critical, quarrelsome; 3) Dependable, self-disciplined; 4) Anxious, easily upset; 5) Open to new experiences, complex; [Anxious, easily upset] and [Calm, emotionally stable]; and 5) Openness: [Open to new experiences, complex]and [Conventional, uncreative].We recoded each variable to range from 0 to 1, such that higher values represent higher levels of each respective trait.
Education.What is your education level?Did not complete HS, HS or GED, Some college, College graduate, Some postgraduate, Postgraduate degree.
We recoded responses to range from 0 to 1, such that higher values represent higher levels of Education.
We recoded responses to range from 0 to 1, such that higher values represent higher levels of Income.
Gender .What is your gender?Female, Male, Other.
We created an indicator variable indicating 0 = Not female and 1 = Female.
Age.What is your age?
We recoded respondents' self-reported Age (in years) to range from 0 to 1.
White.What is your race?White, Black or African-American, American Indian or Alaska Native, Asian, Native Hawaiian or Other Pacific Islander, Some other race, I prefer not to answer.
We created a indicator variable indicating 0 = Not white and 1 = White.
Hispanic.Do you identify as Hispanic or Latino?Yes, No.
We created an indicator variable indicating 0 = Not Hispanic or Latino and 1 = Hispanic or Latino.
Religiosity .How would you classify your level of involvement with your religion or spirituality?Very active, Moderately active, Neither active nor inactive, Moderately inactive, Very inactive.
We reverse coded responses and recoded them to range from 0 to 1, such that higher values represent stronger Religiosity.
Attention Check.Most modern theories of decision making recognize that decisions do not take place in a vacuum.Individual preferences and knowledge, along with situational variables can greatly impact the decision process.To demonstrate that you've read this much, just go ahead and select both red and green among the alternatives below, no matter what your favorite color is.Yes, ignore the question below and select both of those options.What is your favorite color?White, Black, Red, Pink, Green, Blue.
We recoded incorrect responses for White, Black, Pink, and Blue as 0 and correct responses for Red and Green as 1.

Figure SM1 :
Figure SM1: Distribution of 11-Item Numeracy Scale Figure SM2: Distribution of Six-Item Political Knowledge ScaleTable SM3: Political Knowledge x NFCog (without controls) Table SM4: Political Knowledge (Median Split) x NFCog Generally speaking, do you usually think of yourself as Republican, a Democrat, an Independent, or what?We then branched Democrats and Republicans into: Would you call yourself a strong Democrat [strong Republican] or a not very strong Democrat [not very strong Republican]?We branched Independents into: Do you think of yourself as closer to the Democratic Party, Republican Party, or Neither ?We combined responses to create a seven-point scale of Party ID, ranging from 1 = strong Democrat to 7 = strong Republican (with 4 = pure Independent) and recoded the measure to range from 0 to 1.
closely, Very closely, Somewhat closely, Not very closely, Not closely at all.How well would you say you understand the debate over increasing the national debt limit?Extremely well, Very well, Somewhat well, Not very well, Not well at all.How often do you pay attention to what's going on in government and politics?Always, Most of the time, About half the time, Some of the time, Never.

Table SM2 :
Proportion of Correct Responses for Items In the Objective Numeracy Scale with Item and Factor Analyses Person A's risk of getting a disease is 1% in ten years, and Person B's risk is dou-

Table SM2 :
Proportion of Correct Responses for Items In the Objective Numeracy Scale with Item and Factor Analyses BUCKS LOTTERY, the chances of winning a $10.00 prize is 1%.What is your best guess about how many people would win a $10.00 prize if 1,000 people each buy a single ticket to BIG BUCKS?following numbers represents the biggest risk of getting a disease? 1 in 100; 1 in 1000; 1 in 10. 's risk of getting a disease is 1% in ten years, and Person B's risk is double that of A's, what is 's chance of getting a disease is 1 in 100 in ten years, and person B's risk is double that of A's, what is B's risk?Answer : 2 out of 100 0.42 0.39Q8If the chance of getting a disease is 10%, how many people would be expected to get the disease: A: Out of 100? of getting a disease is 10%, how many people would be expected to get the disease: B: Out of 1000?