Quadratic Voting’s Influence on Minority Impact
Current election systems do not ensure efficient results for the whole population. Although they might be fair, as all participants have the same influence on the election outcome, they fail to cater to the people’s different interests and needs. Minority groups are especially disadvantaged under systems like 1-Person-1-Vote (1P1V), as they are subjugated to majority rule. A perfect example of the inefficient results provided by current election mechanisms is the rejection of same-sex marriage through a referendum in California in 2008 (Audi et al., 2008).
Posner and Weyl (2015) argue that adding a quadratic cost to the vote would have inhibited this result, as majority members do not benefit as much from the outcome as minority members do. Quadratic Voting (QV) could be a better election mechanism and protect minorities from results that do not benefit the whole community.
This study’s goal is to evaluate if QV works as a viable alternative to 1P1V for minorities, comparing the impact of participants on election results under both mechanisms. QV could prove itself to be a radical change in how elections occur giving the groups with a lower voice in our society a better chance.
This article was elaborated as a part of a Master's Thesis at the Chair of Strategy and Organization of the Technical University of Munich. See the infographic below for an overview of the work done, continue reading for more detailed information.
THEORY AND HYPOTHESIS DERIVATION
For this study’s scope, a minority is defined as a group whose interest is opposed by a larger group of people. This concept includes ethnic and religious minorities, but also groups like LGBTQI+ community members, entrepreneurs, and scientists.
Precisely the importance and impact of minority groups are often underestimated. Hajnal and Trounstine (2005) show that if the turnout of ethnic minorities had been equal to that of whites in local communities in the United States, a significant number of elections would have had different results. Furthermore, minorities are less likely to vote in localities with a smaller number of minority members (Fraga, 2015), which I argue has to do with the perceived pivotality in the election of the minorities. However, the turnout-gap, the difference in turnout between white and voters from other ethnicities, varies among different minority groups (Fraga, 2015), partly due to cultural reasons (Lapp, 1999). Nonetheless, ensuring representation and inclusion of minorities is vital for a peaceful and just society (Reynolds, 2006).
However, to test to what extent QV could improve the electoral situation of minorities, it is imperative to understand the mechanism and to create a variation that makes it possible to simulate real elections and that assesses the impact of minority members. Lalley and Weyl (2017) propose QV, a mechanism that uses a quadratic cost function to allow participants in an election to buy votes, thus entailing a linear marginal cost function. Rational agents set their marginal benefit equal to the marginal cost to achieve an optimal outcome. This linear relation achieves optimality as voters are forced only to buy votes that increase their chances of being pivotal in an election. This way, individuals show their real preferences and their intensity. However, a fair distribution of resources is needed to ensure an equal price perception by participants.
Because our current society does not provide an equal distribution of resources, it is necessary to consider alternative payment methods, such as introducing an artificial digital currency (tokens). Quarfoot et al. (2017) show that in a one-off election using tokens, QV induces the participants to make trade-offs between candidate policies giving a better expression of preferences. In a case like this, the drivers for making a decision become the budget and candidates. However, in an election setting, there is a chance that participants free-ride, the act of benefitting from goods without spending on them (Hardin, Russell, & Garret Cullity, 2020). Therefore, for this study, I propose a QV mechanism without rebate that uses an artificial currency as a payment method and asks participants to state preferences instead of simulating an election. This change allows assessing the potential impact minorities could have in an election.
Under this mechanism, I state the following hypotheses: Minorities have a larger impact on minority policies under a QV mechanism compared to their impact under 1P1V (Hypothesis 1). The impact of interest groups on the overall election is equivalent (Hypothesis 2). Minorities have a greater impact on minority policies than majority members under QV (Hypothesis 3). Non-minority members have a larger impact on non-minority policies than minority members under QV (Hypothesis 4). Participants are congruent when voting first on 1P1V and then on QV (Hypothesis 5). And lastly, Minorities and Non-minority members behave equally congruent under the proposed experiment design (Hypothesis 6).
METHODOLOGY
The independent variables observed in the study were impact and congruence. Impact is the individual’s share of the total casted votes in an election. Under QV, an individual’s impact on an election may vary, depending on the strength of his or her preference and that of the other participants. Congruence is defined as the participant’s voting coherence between 1P1V and QV. A vote cast on 1P1V should lead to a QV expense carrying the same opinion. Thus, the dependent variables became the policies used, the mechanism being observed, and the affiliation to a minority group (identity).
Depending on the policies being observed, the identity of the participants was segmented differently. In the context where minority policies are analyzed, “Minority” refers to the minority explicitly addressed. For example, in a statement on women quotas in public office, “Women”, and “Mixed” that have self-identified as “Women”, are considered as the minority; all other groups belong to the “Majority.” However, in the context where non-minority policies, like the increase of government spending on green energy, are evaluated; “Minority” refers to all participants identified as a minority group, whereas “Non-Minority” is the label for participants who did not identify with any minority group. Moreover, when observing the overall election results, the individual affiliations were considered.
The experiment used a self-developed web-based application to gather the votes from participants, including the following minorities: women, members of the LGBTQI+ community, entrepreneurs, researchers, and people with migration history. The participant segmentation can be taken from Table 1.
The survey asked participants to state their preferences about the postulated candidate policies to avoid free-riding. First, they had to give their votes under 1P1V and then under QV. The included policies can be seen in Table 2 below. Most of them were taken from the Wahl-O-Mat for the parliamentary elections in Germany (Bundeszentrale für Politische Bildung, 2017), which is a platform that guides the German electorate on upcoming elections using contemporary policies of public concern. Policies not taken from the Wahl-O-Mat were proposed by the author, as they specifically addressed the observed minorities.
RESULTS
I found that minority members had a significantly larger impact on minority policies under QV than on 1P1V. Furthermore, belonging to a minority group did not affect a participants’ overall impact on the election, and the impact of participants changed significantly depending on the policy observed.
Moreover, the impact of “Minority” members was significantly larger than that of “Majority” members on minority policies under QV, albeit being a small effect. Further testing found that policy significantly influenced the participants’ impact on minority policies.
On the other hand, analyzing the impact of minorities on non-minority policies, the candidate policies also had a significant influence on participants’ impact. However, being part of a minority did not significantly change the impact an individual had on non-minority policies compared to “Non-Minority” members.
Furthermore, the congruence of participants was analyzed to assess the validity of the study’s results. The evaluation found that participants significantly did not meet the expected congruence level of “10” (perfect congruence) and that “Minority” and “Non-Minority” members had statistically the same level of congruence, albeit the minorities’ congruence had been a little higher. Furthermore, it was found that most participants spent their budget with token expenditures divisible by five.
In summary, Hypotheses 4 and 5 were rejected, and Hypotheses 1, 2, 3, and 6 could not be rejected. In general terms, minorities had a larger impact on minority policies under QV without losing influence on the overall election. Furthermore, participants behaved incongruently; see Table 3 below for an overview.
DISCUSSION
These results show that the proposed QV mechanism enables the participants to have a higher impact on policies that are more relevant to them, without losing impact on the overall election. This finding is supported by the fact that belonging to a minority group did not influence the impact a participant had on the election. Therefore, I argue that QV is a fair election system. However, the policies included did have a significant influence on the impact of individuals on the election results. It is thus important to include enough interest groups and policies in an election, for the support of participants to spread evenly across the different subjects at hand so as not to generate an unfair situation for any particular minority.
Furthermore, minorities did have a higher impact on minority policies, which speaks in favor of QV serving as a protector of minority groups. Nonetheless, it became evident that the size and cohesion within a minority are also relevant aspects when considering the influence a group could have on election results. An example in this case is the impact level the LGBTQI+ community had on the policy on LGBTQI+ education in schools. The minority consisted of six people, five of whom identified with other minority groups. This spread in preferences led to LGBTQI+ members being the minority group with the largest impact variance. This characteristic resulted in the LGBTQI+ policy being the only minority topic where minority members had an impact smaller than that of the majority. Therefore, the QV mechanism could only avoid majority rule if the minority members share the same interests among the candidate policies and the minority is large enough.
Although QV certainly improves the conditions for minorities in comparison to 1P1V, it is far from ensuring representativeness for minorities, which is ultimately the key factor for a fair and peaceful integration of minorities into society. According to Reynolds (2006), an election system has to consider the minority group’s size, their geographical localization within the observed society, the pre-existence of other ethnical groups, and the actual turnout of the minority groups to be indeed capable of assessing the situation of the minorities and how to devise a system that satisfies their needs. QV fails to achieve this as it focuses on the optimal utility for the whole electorate without paying attention to the unique situation of minorities.
Moreover, minorities and non-minorities alike, failed to behave congruently during the experiment, even though they had the option to change their entries before submitting the survey. This result indicates that the proposed Quadratic Voting mechanism and the restricted budget forced the voters to rethink their priorities and state a new set of preferences when thinking in terms of expenses (Quarfoot et al., 2017; Thaler, 1985). Therefore, the electorate’s opinions on 1P1V do not represent the participants’ real preferences and expose the current system’s weakness (Lalley & Weyl, 2017).
Alternatively, the lack of congruency could be explained by a failure of the participants to understand the QV mechanism and the advantages it entails. This assumption is supported by the linear voting behavior a considerable part of the electorate had on the experiment. Voters spend tokens using numbers divisible by five. This rationality leads to a loss in efficiency because voters fail to recognize the decrease in pivotality their tokens have on high expenditures. Therefore, the question must be raised, if people are capable of thinking in quadratic terms and what consequences this could have for QV applications.
In general terms, QV faces several challenges in the implementation as a protector of minorities. The current social structure lacks a fair distribution of resources. It follows that the implementation of the original mechanism would not guarantee efficiency (Rogers, 2019) and that underbudgeted minorities would struggle under this form of QV. Therefore, the alternative of using an artificial currency is a crucial part of the application. The problem, in this case, lies in how to add value to this currency. In this study, it was attempted to use scarcity and trade-off to assign value to a token. However, this type of mechanism limits applications for QV to closed, one-off, decision-making processes. A use case example was the Colorado Democratic Caucus, which used QV to decide on which policies to implement in 2019 (Rogers, 2019).
Furthermore, a referendum, or a series of referendums, would be the most logical application setting for QV as it would gather the preferences of the whole electorate. However, not many decisions are taken directly to the public in many societies, regardless of the electorate’s discontent with the current political systems. In Germany, for example, there is a lack of identification with the current electoral setup, generating a distancing from politics (Decker et al., 2013). According to Decker et al. (2013), voters feel that their opinion does not influence election outcomes or the policies pursued by politicians. Therefore, there is a need for several reforms to enable a more direct democracy before it would be even possible to think about implementing QV in real-life political decision-making processes.
Limitations
The executed experiment had the following limitations. The sample group consisted of a very young electorate with an academic background. This participant pool could have had similar opinions on political topics, which could have led to a compounding effect on impact. Furthermore, some minority groups’ size was not representative, e.g., the LGBTQI+ community had six participants.
Moreover, answering the survey followed a strict voting order, first under 1P1V and then under QV. To randomize the testing sequence would have provided more transparent results, but this would have made the app’s development more complicated.
However, the most critical limitation was the electorate’s linear voting behavior, which could have been caused by a brief explanation about the QV mechanism included in the experiment. It would have been better to let participants get familiar with QV through more examples before.
Conclusion
This study shows that the proposed QV mechanism functions as an efficient election system that forces the electorate to state its real preferences. Thus, minorities have a higher impact on minority policies without compromising their influence on other topics put up for a vote because the participants’ interests spread among candidate policies. However, the number and type of policies included in an election have a significant influence on the electorate’s behavior and thus, fails to adequately address the needs of minority groups in a political setting. QV focuses on efficient results for the overall population and only protects minorities in the case that it would be detrimental for the population as a whole. Therefore, QV cannot be portrayed as the best mechanism to avoid the tyranny of the majority.
Moreover, this study found that participants had difficulties comprehending how the proposed mechanism functioned and the advantages it entailed, thus failing to act as rational agents when buying votes. This result shows that any implementation of QV requires a good education of the participants first. Because of QV’s complicated execution in the political landscape, it would be better to consider other areas where QV’s advantages could be exploited to its full potential, e.g. market research.
It is advisable to pursue further research on the number of policies included in an election, the number of tokens given out to each participant, and to realize the same analysis under a real election context to evaluate participants’ propensity to free-ride.
References
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