Daria Boratyn, Dariusz Stolicki
10 min
Abstract
Research on the causes of political polarization points towards multiple drivers of the problem, from social and psychological to economic and technological. However, political institutions stand out, because -- while capable of exacerbating or alleviating polarization -- they can be re-engineered more readily than others. Accordingly, we analyze one class of such institutions -- electoral systems -- investigating whether the large-party seat bias found in many common systems (particularly plurality and Jefferson-D'Hondt) exacerbates polarization. Cross-national empirical data being relatively sparse and heavily confounded, we use computational methods: an agent-based Monte Carlo simulation. We model voter behavior over multiple electoral cycles, building upon the classic spatial model, but incorporating other known voter behavior patterns, such as the bandwagon effect, strategic voting, preference updating, retrospective voting, and the thermostatic effect. We confirm our hypothesis that electoral systems with a stronger large-party bias exhibit significantly higher polarization, as measured by the Mehlhaff index.
Alex: That isolation makes sense for testing causality. But walk me through how they set up the voters and parties in this simulation—like, where do they start, and how do voters pick who to vote for?
Sam: They picture opinions on issues as points on a flat map—a two-dimensional space where left-right and other divides show up as positions. Voters and parties each get a spot on that map based on their ideal views; voters like parties closer to their own spot more than far-off ones. This setup is called a spatial policy model. To make it realistic, they mix two kinds of voters: loyal ones clustered near their favorite party's spot, like dedicated fans sticking close to home base, and swing voters spread out more loosely around the center, ready to shift.
Alex: Okay, so a map of opinions with fixed fans and floaters. But what tips a voter's choice when picking a party?
Sam: Voters rank parties by a simple score: divide the party's current seats by how far away it is on the map, raised to a personal power that weighs policy closeness against size. Folks who care more about matching views get a higher power, so distance hurts bigger; strategy fans get a lower one, favoring giants even if farther. This captures real patterns—voters ditching a close small party for a distant big one to avoid waste, or jumping on winners. Dissatisfied ones skip the government entirely first.
Alex: Right—like betting on the frontrunner in a race. Then how do seats get assigned without drawing fake districts?
Sam: They use math shortcuts called seats-votes approximations—formulas that turn total votes into seats as if districts existed, tuned for systems like Jefferson-D’Hondt, which boosts big parties with divisors, or first-past-the-post, where winners take all. No need for thousands of mini-elections; aggregate votes in, biased seats out. This keeps the sim efficient while matching real biases.
Alex: Huh... so that ratio pulls votes to seat-rich parties, their seats grow more via bias, looping tighter. After voting, do positions shift?
Sam: Yes—voters nudge toward their voted party's spot, skewed to pull harder if already close, modeling growing dislike for opposites. Random life tweaks add wiggles, and unhappy government voters push away toward runners-up. Over cycles, bias amplifies this sorting into camps. The paper suggests this mechanism alone drives the polarization they measure.
Alex: So those position shifts after each round—like nudges toward voted parties and pushes from disliked governments—build the sorting. But what decides if a voter even likes the government enough to keep supporting it next time?
Sam: After seats are set, the simulation figures out how well voters think the winning party did in power. They draw a score for overall approval from a range that gets tougher the longer that party stays in charge—like a team wearing down from back-to-back games, losing fans over time. Each voter then gets a personal yes-or-no on that party based on the overall score.
Alex: Okay, government fatigue makes sense—longer in power, more grumbles. So that feeds into the next vote how?
Sam: If a voter dislikes the government's job, they skip voting for it next round, even if its size and closeness would otherwise win them over—like refusing to cheer for a losing coach despite the crowd. This is retrospective voting, judging past performance before picking. It adds balance, as unhappy folks shop rivals instead.
Alex: Right, so no blind loyalty to giants. Then the real sorting kicks in with those preference tweaks—random wiggles, affective pulls, thermostatic pushes. Break down how the affective one works, since you said it's skewed.
Sam: Voters get a small random bump or nothing most times, like daily life nudging opinions slightly off track—but tiny compared to starting spreads. For affective shifts, they move toward their chosen party's spot, but closer voters pull harder while far ones barely budge—like rubber bands snapping fans tight to the team huddle but loosely tugging stragglers. Only satisfied non-government voters or opposition get this; unhappy rulers skip it.
Alex: Huh... so it's not uniform—proximity amps the bandwagon, compressing groups. And the thermostatic flips that for pushback?
Sam: Yes—for dissatisfied government voters, it mirrors but weaker: half-strength push toward their top non-winner, stronger for those already far from it. New spots add all tweaks: random plus affective plus thermostatic. The paper notes this setup, with bias, sorts voters into tighter packs over cycles. But they skip extras like parties moving positions or coalitions to avoid overcomplicating without clear gains—conservative choices that likely understate splits.
Alex: Makes sense—keeps the focus on bias's pull. Isolating that shows meaningful causation without real-world mess. So with all those pieces in place, what did the simulations actually show about how many parties stick around and how voters end up grouped?
Sam: The model first checks if it produces realistic party setups. In setups with small districts—meaning few seats per area, which amps up the large-party edge—the sim ends with just a few surviving parties. This matches patterns in real countries using similar rules, like Poland or the Czech Republic, where big parties dominate despite many running.
Alex: Right, so low seats-per-district squeezes out the small ones, as expected. But does starting spread of voters matter that much?
Sam: They tested sensitivity by tweaking starting values. More spread-out voters at the start actually led to fewer lasting parties—the wide scatter weakens middle options early, speeding their fade. But the core pattern held: stronger bias, tighter fields.
Alex: Huh, counterintuitive on the spread. What about the voter sorting—the polarization measure?
Sam: Under strong bias from small districts, voters formed fewer but much tighter groups around survivors—like marbles settling into deep bowls instead of shallow ones. The paper suggests this boosts the share of differences between groups versus within them, a clear sign of sharper divides. Larger districts, less bias, let more groups linger with softer edges.
Alex: So bias not only prunes parties but packs voters more firmly into what's left. That's a notable link. Did they quantify how much district size—or that bias level—affects the sorting strength?
Sam: They ran a straightforward line fit between average sorting and district seats per area across setups. Each extra seat per area ties to a small drop in sorting, adding up to noticeably less sorting over typical ranges. This setup accounts for a large share of the shifts seen. And it holds for winner-take-all rules too, like in the US—higher concentration there links to more sorting.
Alex: Right, so tweaks like bigger districts could soften the groups. That builds confidence in the mechanism.
Sam: The paper concludes that within its setup, large-party edges push voters into firmer camps over cycles—not just uneven seats, but a real sorter of views. It isolates bias as a contributor to widening gaps. One practical angle: shifting to higher seats per area or even formulas could keep middling options alive longer, easing crowds into extremes and aiding mixed governments.
Alex: Makes sense as a piece of the puzzle we can tweak—not the only cause, but one institutions could address. Overall, this simulation offers a clear view of how seat rules shape divides.
Sam: It does—the evidence suggests meaningful causation there. Thanks for digging into this with me, Alex.
Alex: Pleasure as always, Sam. Thanks for listening to ResearchPod.