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\begin{document}

\title{New Insights on Voter-Party Congruence and Cognitive Ability: A Genetically Informed Approach}

\author{}
\date{}

\maketitle

%\author[1]{Asya Bülbül}
%\affil[1]{Department of Government, Uppsala University, Uppsala, Sweden\\
%\texttt{asya.bulbul@statsvet.uu.se}}
%date{} % <-- removes the date
%\maketitle 






\appendix
\section{Appendix}
\label{sec:appendix}

\subsection{Congruence Analyses using CHES and SALTY surveys}
\label{sec:correlations}

\begin{table}[H]
\centering
\caption{Correlations of CHES Party Positions and MP Survey Averages}
\setlength{\tabcolsep}{20pt} % default is ~6pt
\begin{tabular}{l r}
\toprule
CHES-MP Survey & Correlation Coefficient \\
\midrule
Social issues           & -0.43 \\
Deregulation issues     & -0.66 \\
Redistribution issues   &  0.97 \\
Immigration issues      & -0.74 \\
Taxation issues         & -0.99 \\
EU issues               &  0.98 \\
Left-Right position     &  0.97 \\
\bottomrule
\end{tabular}
\end{table}



\subsubsection{Issue Match of CHES and SALTY}
\label{sec:CHEScalculations}

\begin{table}[H]
\caption{Comparison of Policy Positions in 2006 CHES and 2009-2010 SALTY Questionnaires}
\centering
\begin{tabular}{p{0.2\textwidth}p{0.35\textwidth}p{0.35\textwidth}}
\toprule
\textbf{Category} & \textbf{2006 CHES Questionnaire} & \textbf{2009-2010 SALTY Questionnaire} \\
\midrule
\textbf{Social Life} & Position on social lifestyle (e.g., homosexuality) & Limit the right to free abortion \\
\midrule
\textbf{Deregulation} & Position on deregulation of markets & 
Decrease the public sector; Sell public companies; Expand private companies in healthcare and education; Increase freedom for private companies; Reduce financial market influence on politics; Introduce a 6-hour workday \\
\midrule
\textbf{Redistribution} & Position on redistribution from the rich to the poor & Decrease economic inequality \\
\midrule
\textbf{Public Services} & Position on improving public services vs. reducing taxes & 
Decrease taxes; Reduce welfare benefits \\
\midrule
\textbf{Urban vs. Rural} & Position on urban vs. rural interests & Increase economic support for rural areas \\
\midrule
\textbf{Immigration} & Position on immigration policy & Accept fewer refugees; Increase labor immigration; Require language tests for citizenship  \\
\midrule
\textbf{Multiculturalism} & Position on integration of immigrants (multiculturalism vs. assimilation) & Support cultural preservation among immigrants \\
\midrule
\textbf{EU} & Orientation of party leadership towards European integration & Sweden should leave the EU\\
\bottomrule
\end{tabular}

\begin{tablenotes}
\small
\item Note: All SALTY issues are recoded to the same range as CHES and are adjusted for polarity to align with CHES issues.
\end{tablenotes}
\end{table}

There are several potential limitations to matching these two datasets on policy issues. First, the measurement scales differ between CHES (0-10) and SALTY (1-5). To make them more comparable, the SALTY scale is normalized to range from 0 to 10. This means that it is very unlikely that there will ever be an exact value of zero for perfect congruence, meaning that this approach provides only an imperfect measure of congruence. Additionally, some differences in the ways that the questions are worded could present another challenge, complicating the alignment between the datasets. This issue is partially mitigated by including only one question when it almost perfectly matches the CHES question, or by averaging multiple related questions to form a policy group that corresponds more closely to CHES categories

\subsubsection{General Congruence Levels}

\begin{figure}[H] % Use positioning hints
\centering
\includegraphics[width=0.9\textwidth]{Graph general.png} % cleaner syntax
\caption{Levels of congruence among DZ twins.}
\label{fig:levels2}
\begin{minipage}{0.8\textwidth}
\small
\textit{Note:} All alignment variables range from 0 to 10. 
\end{minipage}
\end{figure}

Left-right alignment has the highest overall average, indicating that a good alignment along the left-right axis between the parties and the voters is the most prominent one within the population. However, this might partly be due to the better overlap between the CHES and SALTY left-right scale measurement. As for the specific issue positions, people seem to be decently aligned with the party they voted for. 


\begin{figure}[H]
\centering
\resizebox{0.9\textwidth}{!}{
\includegraphics{coefplot_graph1 (2).png}
}
\caption{Within and between family analyses}
\label{fig:bf-wf1}
\vspace{0.5em}
\begin{minipage}{0.8\textwidth}
\small
\textit{Note:} *** \(p<0.001\), ** \(p<0.01\), * \(p<0.05\). 
Between-family models include controls for sex, birth year, the interaction between sex and birth year, and the first ten principal components of the genetic-relatedness matrix. 
The within-family models include controls for sex and sibling-pair fixed effects. Number of observations for within and between family analyses are \textasciitilde 2,600 DZ twins and \textasciitilde 1,300 twin pairs. 
\end{minipage}
\end{figure}

Except on social issues and deregulation issues, all between-family models indicate that a positive relationship between cognitive ability PGI and voter-party congruence is substantively strong and significant. However, after controlling for shared genetic and environmental factors with sibling-pair fixed effects, the positive effect diminishes for alignment on economic issues, meaning that between-family effects were minimally confounded. Nevertheless, for left-right, EU issue, rural issue and immigration issue congruences, the positive effect of the cognitive ability remains significant. The within-family results show that a one-standard-deviation increase in CP PGI corresponds to an increase of approximately 13\% of a standard deviation in left-right congruence, 8\% of a standard deviation in EU issue congruence, 7\% of a standard deviation in rural issue congruence and 15\% of the standard deviation in immigration congruence. 





\begin{table}[H]
\centering
\caption{Results for Mediation with CHES data}
\label{tab:mediation_results}
\begin{threeparttable}
\begin{tabular}{lcccc}
\toprule
\textbf{Variable} & \multicolumn{2}{c}{\textbf{LR Congruence}} & \multicolumn{2}{c}{\textbf{EU Congruence}} \\
\cmidrule(lr){2-3} \cmidrule(lr){4-5}
& (1) & (2) & (1) & (2) \\
\midrule
\multicolumn{5}{l}{\textbf{Cognitive Performance}} \\
CP PGI (Main Sample) & 0.13\textsuperscript{***} &  & 0.08\textsuperscript{*} &  \\
                           & [0.10]                   &                    & [0.06]                   &  \\
CP PGI & 0.32\textsuperscript{***} & 0.30\textsuperscript{***} & 0.15\textsuperscript{*} & 0.14 \\
       & [0.08]                    & [0.08]                    & [0.08]                   & [0.08] \\
Cognitive Performance Trait &     & 0.06                      &                          & 0.05\textsuperscript{} \\
                             &     & [0.04]                   &                          & [0.04] \\
\% mediated & \multicolumn{2}{c}{6.99\%} & \multicolumn{2}{c}{11.87\%} \\
\textit{N} & \multicolumn{2}{c}{552} & \multicolumn{2}{c}{552} \\
\midrule
\textbf{Variable} & \multicolumn{2}{c}{\textbf{Immigration Congruence}} & \multicolumn{2}{c}{\textbf{Rural Congruence}} \\
\cmidrule(lr){2-3} \cmidrule(lr){4-5}
& (1) & (2) & (1) & (2) \\
\midrule
\multicolumn{5}{l}{\textbf{Cognitive Performance}} \\
CP PGI (Main Sample) & 0.10\textsuperscript{**} &  & 0.7\textsuperscript{*} &  \\
                           & [0.10]                   &       & [0.06]          &  \\
CP PGI & 0.12\textsuperscript{} & 0.09       & 0.08      & 0.05      \\
       & [0.08]      & [0.08]      & [0.07]      & [0.08]      \\
Cognitive Performance Trait &     & 0.08    &     & 0.07    \\
                             &     & [0.04]    &     & [0.04]    \\
\% mediated & \multicolumn{2}{c}{24.16\%} & \multicolumn{2}{c}{31.44\%} \\
\textit{N} & \multicolumn{2}{c}{552} & \multicolumn{2}{c}{552} \\
\midrule
\textbf{Variable} &  & \multicolumn{2}{c}{\textbf{Multicultural Congruence}} & \\
\cmidrule(lr){3-4}
                  &  & (1) & (2) & \\
\midrule
\multicolumn{2}{l}{\textbf{Cognitive Performance}} &  &  & \\
CP PGI (Main Sample) &  & 0.14\textsuperscript{***} &                & \\
                     &  & [0.10]                 &                     & \\
CP PGI               &  & 0.07                   & 0.06                    & \\
                     &  & [0.09]                 & [0.08]                  & \\
Cognitive Performance Trait &  &                  & 0.06                    & \\
                             &  &                  & [0.04]                  & \\
\% mediated          &  & \multicolumn{2}{c}{21.27\%} & \\
\textit{N}           &  & \multicolumn{2}{c}{548}     & \\
\bottomrule
\end{tabular}
\begin{tablenotes}
\small
\item Note: Standard errors in parentheses. *** \(p<0.001\), ** \(p<0.01\), * \(p<0.05\).Due to the smaller sample size of mediation analyses, some of the significances of main effects observed in the main sample have vanished. Nevertheless, they are mostly comparable in terms of their size to the smaller mediation sample.
\end{tablenotes}
\end{threeparttable}
\end{table}


The percentage of mediation is very low for the left-right congruence score at around 8\%, meaning that CP PGI influences alignment based on left-right identification through possibly different pathways other than cognitive performance (same as the Riksdag sample results). As for the three other issue positions, the percentage of mediation is relatively high for rural issue congruence score at 31\% and for immigration issues congruence score at 25\%, followed by EU congruence at 12\% being the lowest. These findings suggest that, in the case of left–right congruence and rural issue congruence, there may be an additional trait, possibly independent of cognitive ability that causally influences high congruence scores. However, cognitive ability does appear to play a more relevant role in shaping congruence toward specific issues, particularly on rural and immigration policies.




\subsection{Descriptives of DZ Twins}

\begin{table}[H]\centering
\def\sym#1{\ifmmode^{#1}\else\(^{#1}\)\fi}
\caption{Descriptive Statistics}
\begin{tabular}{l*{1}{ccccc}}
\toprule
                    &        mean&          sd&         min&         max&       count\\
\midrule
Standardized values of (congr\_rpublic)     &       0.015&       1.000&       -2.96&        1.22&        3395\\
Standardized values of (congr\_nato)     &       0.006&       1.017&       -3.28&        1.30&        3381\\
Standardized values of (congr\_defense)     &      -0.006&       1.018&       -4.16&        1.23&        3409\\
Standardized values of (congr\_euro)     &      -0.026&       1.015&       -2.71&        1.20&        3419\\
Standardized values of (congr\_eu)     &      -0.036&       1.023&       -2.59&        1.17&        3426\\
Standardized values of (congr\_refugees)     &      -0.003&       1.005&       -2.48&        1.40&        3431\\
Standardized values of (congr\_innercity)     &      -0.008&       1.000&       -2.99&        1.18&        3433\\
Standardized values of (congr\_nuclear)     &      -0.003&       0.997&       -2.82&        1.28&        3426\\
Standardized values of (congr\_pornog)     &       0.013&       0.997&       -1.71&        1.61&        3442\\
Standardized values of (congr\_sixhour)     &       0.007&       0.994&       -2.23&        1.25&        3437\\
Standardized values of (congr\_privatehealth)     &       0.015&       0.987&       -3.08&        1.26&        3402\\
Standardized values of (congr\_rincome)     &       0.003&       1.012&       -4.22&        1.16&        3435\\
Standardized values of (congr\_taxes)     &      -0.002&       0.998&       -3.04&        1.22&        3413\\
Standardized values of (LR\_distance)     &      -0.015&       1.004&       -6.03&        1.18&        3447\\
CP PGI              &       0.023&       1.017&       -4.15&        3.44&        3768\\
Female=1            &       0.548&       0.498&        0.00&        1.00&        3821\\
Age                 &      59.437&       4.511&       51.00&       66.00&        3821\\
PC1                 &      -0.001&       0.011&       -0.05&        0.04&        3768\\
PC2                 &      -0.001&       0.010&       -0.06&        0.05&        3768\\
PC3                 &       0.001&       0.010&       -0.07&        0.07&        3768\\
PC4                 &      -0.000&       0.011&       -0.11&        0.06&        3768\\
PC5                 &       0.000&       0.010&       -0.05&        0.08&        3768\\
PC6                 &       0.000&       0.010&       -0.08&        0.06&        3768\\
PC7                 &      -0.000&       0.011&       -0.09&        0.08&        3768\\
PC8                 &      -0.000&       0.011&       -0.10&        0.06&        3768\\
PC9                 &      -0.000&       0.010&       -0.09&        0.07&        3768\\
PC10                &      -0.000&       0.010&       -0.04&        0.07&        3768\\
\bottomrule
\end{tabular}
\end{table}


%\begin{figure}[H]
%\centering
%\resizebox{0.9\textwidth}{!}{%
%\includegraphics{histsalty.png}
%}
%\caption{Distribution of responses for each policy item for DZ twins}
%\label{fig:salty}
%\end{figure}

\subsubsection{Party Descriptives in SALTY}
\begin{figure}[H]
\centering
\resizebox{0.9\textwidth}{!}{%
\includegraphics{hist_partypreference.png}
}
\caption{Descriptive for each party on the number of voters they have for DZ twins}
\label{fig:preference}
\end{figure}


\subsection{Issue Questions in SALTY and MP Survey}
\label{sec:question}

\begin{table}[H]
\centering
\begin{threeparttable}
\caption{SALTY and Riksdag MP Survey corresponding items}
\rowcolors{2}{gray!15}{white}
\begin{tabular}{p{6.5cm} | p{6.5cm}}
\hline
\textbf{Swedish} & \textbf{English} \\
\hline
Minska den offentliga sektorn & Reduce the public sector \\
Minska försvarsutgifterna & Reduce defense spending \\
Minska inkomstskillnaderna i samhället & Reduce income differences in society \\
Bedriva mer av sjukvården i privat regi & Conduct more of healthcare in private management \\
Införa sex timmars arbetsdag för alla & Introduce a six-hour working day for everyone \\
Förbjuda alla former av pornografi & Prohibit all forms of pornography \\
Ta emot färre flyktingar i Sverige & Accept fewer refugees in Sweden \\
Sänka skatterna & Lower taxes \\
Stoppa privatbilismen i innerstäderna & Stop private car traffic in inner cities \\
Sverige bör på lång sikt avveckla kärnkraften & Sweden should, in the long term, phase out nuclear power \\
Sverige bör införa euron som valuta & Sweden should adopt the euro as its currency \\
Sverige bör utträda ur EU & Sweden should leave the EU \\
Sverige bör söka medlemskap i Nato & Sweden should apply for NATO membership \\
\hline
\end{tabular}
\begin{tablenotes}
\footnotesize
\item \textit{Note:} Respondents rated each proposal on a scale from 1 to 5, where 1 = \textbf{Very bad proposal} and 5 = \textbf{Very good proposal}. Intermediate values represent gradations of agreement.
\item Swedish items are taken directly from the original surveys of SALTY 2010 and Riksdag MP Survey 2006; English translations are provided for reference.
\end{tablenotes}
\end{threeparttable}
\end{table}


\subsection{Analyses for adaptation at the party level}
\label{sec:adaptation2}


\begin{table}[H]
\centering
\caption{Results for Turnout Mediation}
\label{tab:mediation_results}
\begin{threeparttable}
\begin{tabular}{lcccc}
\toprule
\textbf{Variable} & \multicolumn{2}{c}{\textbf{Left-Right }} & \multicolumn{2}{c}{\textbf{EU Membership }} \\
\cmidrule(lr){2-3} \cmidrule(lr){4-5}
& (1) & (2) & (1) & (2) \\
\midrule
\multicolumn{5}{l}{\textbf{Cognitive Ability}} \\
CA-PGI               & 0.14\textsuperscript{***}  & 0.14\textsuperscript{***}  & 0.10\textsuperscript{**} & 0.10\textsuperscript{**} \\
                     & [0.04]                     & [0.04]                     & [0.04]                   & [0.04] \\
Voter Turnout        &                            & 0.25                       &                          & -0.06 \\
                     &                            & [0.22]                     &                          & [0.20] \\
\% mediated          & \multicolumn{2}{c}{-0.8\%} & \multicolumn{2}{c}{0.3\%} \\
\textit{N}           & \multicolumn{2}{c}{2{,}444} & \multicolumn{2}{c}{2{,}478} \\
\midrule
\textbf{Variable} & \multicolumn{2}{c}{\textbf{Refugee Acceptance }} & \multicolumn{2}{c}{\textbf{Six-hour Workday}} \\
\cmidrule(lr){2-3} \cmidrule(lr){4-5}
& (1) & (2) & (1) & (2) \\
\midrule
\multicolumn{5}{l}{\textbf{Cognitive Ability}} \\
CA-PGI              & 0.12\textsuperscript{***}  & 0.12\textsuperscript{***}  & 0.11\textsuperscript{**} & 0.11\textsuperscript{**} \\
                     & [0.04]                     & [0.04]                     & [0.04]                   & [0.04] \\
Voter Turnout        &                            & 0.46\textsuperscript{*}    &                          & -0.06 \\
                     &                            & [0.19]                     &                          & [0.21] \\
\% mediated          & \multicolumn{2}{c}{-2.1\%} & \multicolumn{2}{c}{0.3\%} \\
\textit{N}           & \multicolumn{2}{c}{2{,}488} & \multicolumn{2}{c}{2{,}498} \\
\bottomrule
\end{tabular}
\begin{tablenotes}
\small
\item Note: *** \(p<0.001\), ** \(p<0.01\), * \(p<0.05\) Standard errors in parentheses. Analyses conducted with twin-pair FE.
\end{tablenotes}
\end{threeparttable}
\end{table}



\subsection{What is a PGI?}
\label{sec:PGIs}
To understand how PGI is constructed, we should start with the basics of genetics. The human genome is contained within the nucleus of every cell, and in every nucleus, there are 23 pairs of chromosomes (46 in total), each pair inherited from each parent. Each chromosome is made up of DNA (deoxyribonucleic acid). DNA is what carries the genetic instructions and it is composed of two strands that coil around each other to form a double helix. These strands are made up of simpler molecules called nucleotides (adenine (A), thymine (T), cytosine (C), and guanine (G)). A always pairs up with T and C pairs up with G, however, the sequence in which these base pairs appear along the DNA strand can vary. 99.9\% of our genome is identical, meaning that 99.9\% of the nucleotide sequences in our DNA are the same across different people. However, that little 0.01\% variance in our DNA is what accounts for all of our genetic diversity. These variations in our DNA make each person unique, affecting everything from physical appearance to susceptibility to diseases, and as the socioeconomics literature also shows, to differences in political and social traits. The most common type of genetic variation is Single Nucleotide Polymorphisms (SNPs), where a single nucleotide differs between individuals. For instance, one person might have an adenine (A) at a specific position in the DNA, while another might have a cytosine (C) at the same position. These different forms of the same gene are also referred to as alleles, and in this example, there are two alleles at this SNP: A and C. However, since humans have two sets of chromosomes—one set inherited from each parent, each individual has two alleles at each SNP (such as AA, CC or AC). In a population, the most common allele at a locus (location) is called the major allele, and the less common one is called the minor allele. \footnote{For instance, if 80\% of the alleles at one particular position in a given population are Adenine(A), it is a major allele, and if 20\% of the alleles at that same position is Cytosine(C), that is a minor allele. } Depending on whether an individual has zero, one, or two copies of the minor allele \footnote{Minor alleles provide a clearer contrast for detecting genetic associations. In many populations, the major allele is so common that almost everyone has at least one copy, making it harder to discern its influence. The presence or absence of a minor allele can more distinctly show correlations with specific traits or conditions.}, alleles at a locus are coded as 0, 1, or 2. When constructing a PGI, it is essential to count how many of each trait allele (allele that is associated with the trait at a particular SNP) a person has. The count of these alleles (0, 1, or 2) at each SNP reflects the degree of genetic influence that SNP has on the trait. For instance, the minor allele “A” at an SNP1 might be associated with a higher BMI (body mass index) and individuals with two copies of this minor allele (AA-coded as 2) would, on average, have a higher BMI than those with one or no copies. However, not every SNP has an impact, or the same impact on the trait, which also needs to be accounted for. The information for identifying which SNPs are associated with the target trait is obtained from large-scale studies called Genome-Wide Association Studies (GWAS). In GWAS, researchers test the association between millions of SNPs and a specific trait (measured by disease status, body height, or response to a survey question for social traits). Put simply, in GWAS the sample of individuals is the unit of analysis. In this setup, SNPs serve as the independent variables, while the traits of interest act as the dependent variables. Each SNP is typically analyzed one by one in terms of its association with the trait (through regression analysis) meaning that each SNP is a separate hypothesis being tested against the outcome trait. Because the human genome contains millions of SNPs, GWAS involves performing millions of independent regression analyses, which means that the possibility of encountering "false positives” increases, making it necessary for a stringent p-value. Therefore, A SNP is considered to be “genome-wide significant” for the trait if the p-value associated with its effect on the outcome is less than 5 in 100 million (p < 5 × 108). In the end, the allele count is multiplied (or weighted) with the estimated effect of that SNP (how much SNP correlates with the trait). Thus, a polygenic index for an individual i is the sum of minor alleles xij at SNP j, weighted by the beta coefficient (estimated effect) of SNP j. Typically, the resulting index will then be standardized so that the average score is set to zero and the standard deviation is set to one. 

In the end, the formula for a person’s PGI is: 


\begin{equation}
PGI_i = \sum_{j=1}^{J} \beta_j \times x_{ij}
\end{equation}


This PGI score can then be used like any other measurable personal characteristic in statistical models to estimate the genetic likelihood for a particular trait. 

A PGI might not only capture causal genetic effects when it is used just as an independent variable without any controls. It can capture population stratification and genetic nurture effects, which would confound the causal relationship. First, there can be (and will be) population group identifiers or genetic backgrounds that are associated with the genotype that needs to be accounted for. In a larger context, this can occur when a study's sample includes individuals from different ancestral or ethnic groups that have different allele frequencies. A famous example is the “chopstick gene” by Hamer and Sirota (2000). When we do not account for population stratification in a study that compares the Asian population with a non-Asian population for instance, we might find a certain genetic variant that appears to be significantly associated with chopstick-using skill. However, the association would actually arise because the gene is more prevalent in the Asian population that, for cultural reasons, is more likely to use chopsticks, not because there is a chopstick gene. It is also important to note that population stratification can occur even in ethnically homogenous societies due to geographic isolation\footnote{Geographic barriers limit the interaction of groups of people, leading to genetic differentiation.}, social stratification\footnote{Social stratification based on class education etc. can result in genetic stratification due to mating preferences within one’s own socio-economic circle (e.g. assortative mating).}, and phenomena such as genetic drift\footnote{Genetic drift is a process where random exogenous factors (bottleneck effect) or a small group's separation from a larger population (founder effect) leads to changes in allele frequencies over time. This can occur due to natural disasters, human conflicts, or simply by chance when a few individuals start a new population. (Mills, Barban, & Tropf, 2020)}, which significantly influences the genetic structure of populations. Secondly, there’s the issue of genetic nurture (a type of passive gene-environment correlation), where unmeasured parental genes influence the child’s environment. For instance, genetic variance found in parents might lead them to foster certain environments which would lead to the same trait in the offspring, nevertheless, it would be a false appearance of genetic transmission. Both of these issues (population stratification and genetic nurture effects), however, will be substantially reduced if researchers have access to the parental genotypes or sibling genotypes. When sibling data is available, applying sibling fixed effects allows for the control of shared genetic and environmental influences that address population stratification and genetic nurture problems, isolating the effect of interest (see Ahlskog et al., 2022; Dawes et al., 2021), Since siblings share many of the same environmental factors shaped by parental genetics, sibling fixed effects can reduce the influence of genetic nurture effects. Population stratification is also controlled because siblings are by nature members of the same subpopulation (the same family) which eliminates the risk that population-based differences are being mistaken for genetic effects. 

There can also be problems with the measurement of the PGI due to the finite sample size. In GWAS, estimated genetic effects are used as weights to build the PGI. The accuracy of these weights, and thus the PGI itself, relies heavily on the sample size of the GWAS. A larger sample size generally allows for a more precise estimation of these genetic effects. Although the sample size of GWAS is large and gets bigger every year, it still lacks data from many parts of the world, therefore, as the way it is, PGIs estimated from current GWAS is unable to represent the true genetic variation. This is called attenuation bias, which means the estimated relationship between the PGI and the trait is biased towards zero, meaning that it is showing weaker than the true relationship.
 

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