What the evidence says
The available evidence on supermajority requirements comes from a single formal/simulation study of legislative decision-making under polarization (Millar-Sáez 2026). Its central finding is that raising the approval threshold from simple to supermajority does not act as a neutral procedural brake — it interacts with how divided a legislature already is. Under high quorum requirements, the approval rate for proposals "can collapse when p is low," which the study describes as the institutional requirement amplifying existing fragmentation rather than simply making agreement harder across the board. The same mechanism shows up in output terms: more demanding majorities "decrease the number of proposals passed and, in certain scenarios, the aggregate social welfare."
A second strand of the same study traces this through a specific channel: minority veto power. Under supermajority thresholds, "the minority bloc acquires structural veto power, as its refusal to cooperate prevents the required quorum from being reached." This gives a concrete mechanism for the output and approval-rate declines above — it is not that supermajority rules make consensus marginally harder, but that they hand a blocking minority the ability to withhold the votes needed to reach quorum at all.
The study also reports a threshold-like dynamic in efficiency specifically under a two-thirds supermajority rule: average efficiency "remains relatively stable in Phases III and IV, but collapses abruptly upon entering Phase V" as the share of independent legislators grows. Consistent with this, the study reports that simple majority is "the only one that guarantees sustained efficiency" in highly polarized contexts, and attributes this to independents under moderate thresholds favoring "more inclusive negotiation dynamics" — implying the mechanism runs through how independents can be incorporated into winning coalitions under different threshold rules.
Finally, the study reports that in polarized configurations, certain high quorums fail to reach an efficiency maximum at all: "strict rules can prevent the very existence of an efficient equilibrium." This is a stronger claim than a magnitude reduction — it states that for some supermajority/polarization combinations, no efficient outcome exists in the model, not merely a less efficient one.
All of these findings come from one source using a formal/simulation design (confidence tier A per the claim set, direction confidence high, magnitude confidence mostly medium). No claim here addresses direct democracy specifically — ballot initiatives, referenda, or citizen-proposed measures — despite that being the framing of this topic; every claim concerns legislative (parliamentary) supermajority rules. Likewise, no claim in this set addresses the single-subject gate at all — its effects on approval rates, output, or drafting behavior are absent from the evidence base.