Electoral thresholds

Why can a party winning one voter in twenty end up with no seats at all?

Proportional representation makes a simple promise: seats in proportion to votes. Five percent of the votes, five percent of the seats. Yet in Germany's 2013 federal election the Free Democrats took 4.8 percent and won nothing, the AfD took 4.7 percent and won nothing, and altogether around fifteen percent of the ballots cast elected nobody at all.

That is not a rounding error and it is not a failure of the arithmetic. It is the system working exactly as written. So the question worth sitting with is not "why was it unfair" but something more mechanical: what happens to a proportional formula when you bolt a cutoff onto the front of it?

Consider what a threshold actually is. Almost everything else in an election is continuous — one more vote nudges a party's share up by a hair, and under pure proportionality nudges its seat count by a matching hair. A threshold inserts a single point on that line where the output jumps.

Below it, a party's votes are not merely worth less. They are removed from the calculation entirely. Ask what happens to the seats those votes would have won. They do not vanish; the chamber still has all its seats. They are redistributed among the parties that cleared the bar.

Now hold that in mind, because it is the part people miss. A threshold is not only a penalty on small parties. It is simultaneously a bonus to large ones, and the bonus is exactly the size of the discarded vote. If a sixth of the ballots are set aside, every qualifying party's seat share is inflated by roughly a fifth relative to its vote share. The 2013 Bundestag produced a coalition holding about eighty percent of seats on around sixty-seven percent of votes, and the discarded ballots are where the gap came from.

Why would anyone build this deliberately? Push on the alternative. In a chamber with no cutoff, any faction able to gather a single seat's worth of votes gets a seat — and if the large parties are close, a party of one or two seats can hold the balance and name its price. The stated rationale in post-war Germany was governability: keeping the chamber from splintering into a dozen micro-parties that make coalition formation slow and fragile, with the Weimar Republic's fragmented Reichstag as the cautionary case. Whether the threshold genuinely delivers stability, or mainly protects incumbents, is argued about seriously by political scientists, and I would not pretend it is settled.

Now the part I find most instructive: the cutoff changes voters before it changes seats. If you support a party polling at 4 percent, your vote is not worth 4 percent of a normal vote — it is worth roughly nothing unless enough others join you. So you may vote for your second choice instead, which pushes your first choice further down, which convinces the next voter to defect too. The threshold does not merely measure support; it participates in creating it. In Germany the reverse tactic is a recognised campaign move, with large-party supporters lending their list vote to a small partner to keep it above five.

And notice that a written threshold is not the only kind. The Netherlands sets no legal cutoff, but its 150-seat chamber still has an arithmetic floor of about 0.67 percent, because that is what one seat costs. Any district-based system carries an effective threshold set by district size. The legal number simply makes explicit a bar that geography imposes anyway.

A few refinements.

The threshold is a design dial, not a constant. Israel raised its bar from 2 percent to 3.25 percent in 2014; Turkey lowered its unusually high 10 percent bar to 7 percent in 2022; Poland uses 5 percent for parties and 8 percent for coalitions, which quietly penalises the very alliances that clearing the bar would otherwise encourage.

Second, real systems often soften the cliff rather than remove it. Germany's basic-mandate clause lets a party that wins three constituency seats receive its full proportional entitlement even below 5 percent — which is how Die Linke, on 4.9 percent in 2021, still sat with a proportionate delegation. That clause was deleted in a 2023 reform and then restored by the Federal Constitutional Court in 2024, which is a good indication that where exactly the cliff should sit is a live constitutional question, not a technicality.

Third, resist the tempting misreading that below-threshold votes are "wasted" in the ordinary sense. Wasted usually means surplus — votes beyond what a winner needed. These are different: they are votes that actively strengthened the parties their casters opposed. The transfer is the mechanism, and it is what makes the cutoff a much sharper instrument than its small number suggests.

• How different seat-allocation formulas — D'Hondt, Sainte-Lague, largest remainder — add their own implicit bias on top of the legal threshold.
• Duverger's law, and whether a threshold's real effect runs through strategic voters rather than through the arithmetic.
• Mixed-member systems, where a constituency win can bypass the list cutoff entirely.

Every term the collection defines is gathered in the glossary.