In fact, the strong biases built into the Catalan electoral system elevated the crisis by inflating the secessionists’ parliamentary majority. And these same rules may perpetuate the crisis.

After the declaration of independence, Spain’s central government used its powers under Article 155 of the constitution to take control of the regional government. Madrid called for fresh regional elections on Dec. 21. But Catalonia’s separatists may win a parliamentary majority again, even if they lose at the polls.

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The fine print of electoral rules matters

The Catalan parliament is elected via proportional representation, which is commonly used around the world. Why did this “proportional” system lead to a surprise advantage for separatists? It’s all in the fine print.

Voting in Catalonia is straightforward; voters cast their ballots for a single party list. Seats are then allocated to the winning parties proportionally within each of Catalonia’s four provinces. Parties must win more than 3 percent of the vote in a province to be eligible to gain seats in that province.

In the 2015 Catalan regional elections, separatists won 48 percent of the vote but elected 53 percent of the 135 deputies. But how did separatists claim 72 seats, a majority?

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For starters, seats aren’t distributed evenly across the four provinces. Catalonia’s severe malapportionment means Barcelona Province, the most populous and pro-Spanish, has 14 fewer deputies than it should have, based on population. The three more rural provinces — Girona, Lleida and Tarragona — where separatist parties perform more strongly are correspondingly overrepresented.

Had the 135 seats been allocated evenly across Catalonia, the results would be different. This built-in malapportionment shifted two seats from the nonseparatist to the separatist camp, thus nearly doubling the separatist parliamentary majority from five to nine seats.

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The Catalan parliament proposed to hold an Oct. 1 independence referendum, which Spain’s Constitutional Court declared illegal. The measure passed with 72 of the 135 deputies in favor. The parliament’s actual vote for unilateral declaration of independence on Oct. 27 was closer, with only 70 deputies in favor. Eliminating malapportionment would have left separatists with a three-vote majority on the referendum but the absolute bare minimum for independence — making the unilateral declaration a much dicier proposition.

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What does the electoral formula tell us?

Catalonia uses the common d’Hondt formula of proportional representation. The formula’s bias toward large parties aided separatists, who combined to support the Together for Yes (JxSí) coalition. The smaller pro-separatist, anti-capitalist Popular Unity Candidacy (CUP) also won seats. Four non-separatist parties captured most of the remaining votes. The largest, the vehemently anti-separatist Citizens, had less than half of the support of Together for Yes.

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Would this have been different under the Ste. Laguë formula, a less biased option? Yes, a simulated analysis shows that, despite Barcelona’s underrepresentation, secessionists would have had three fewer deputies under the Ste. Laguë formula, cutting their majority by two-thirds, from nine seats to three.

If Barcelona had as many deputies as it merits based on population, Ste. Laguë would have given separatist formations four fewer seats, leaving them with a wafer-thin one-seat majority. Defections from separatists suggest that the UDI vote would not have passed with a one-seat majority.

Districts also have an impact

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Some countries, like the Netherlands, treat the country as a single constituency. Catalonia follows the model used in Spanish national elections, and each province serves as a separate electoral constituency or district. Like the d’Hondt approach, multiple constituencies that vary in size aid large parties in the smaller constituencies. The regional election split Catalonia into four districts, giving an advantage to the larger Together for Yes coalition.

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The number of deputies up for election in a constituency determines the vote share needed for a seat. The smaller the number, the higher the share because there are fewer seats to go around. In Lleida, parties need to win 6.3 percent of the popular vote to be certain to win one of the 15 seats — several multiples of the 1.2 percent that would be required in Barcelona (if the election law did not separately require that parties win 3 percent of the vote to be eligible to receive seats).

Similarly, fewer seats tend to result in larger parties gaining a disproportionate share. For example, a party that wins 51 percent in a three-seat constituency receives two seats — not winner-take-all, but still nearly 16 percent more than its fair share. Outcomes like this occur regularly in small provinces in Spanish parliamentary elections.

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What does this all mean, in terms of actual votes per seat? In 2015, separatist parties “paid” significantly fewer votes per seat in all three rural provinces. Across Catalonia, separatists “paid” 4,060 fewer votes per seat than they would have in a completely fair allocation of votes.

A single Catalonia-wide district would have been much less favorable to separatists. Depending upon the electoral formula, it would have either sliced their majority down to one seat (d’Hondt) or left them one seat short of a majority (Ste. Laguë). Either way, the drive for independence would have been severely impeded.

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And don’t forget about that 3 percent threshold

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The 3 percent threshold to qualify for seats eliminated the non-separatist Democratic Union of Catalonia (UDC) from contention outside of Lleida Province, where it still couldn’t win a seat. In the single district scenario, reducing the threshold to 2 percent would have caused separatists to lag behind their opponents by either four (d’Hondt) or five (Ste. Laguë) seats, making any parliamentary action toward independence hard to envision.

All of these same rules will apply during the Dec. 21 election. Early poll results indicate that separatists may yet again win a majority even though they splintered back into multiple parties and have fallen further behind relative to non-separatist parties. It has happened before: In 1999, the Catalan government won reelection despite losing the popular vote.

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Although separatists would lack a mandate to follow through with secession, they would have the right to govern in Catalonia and the ability to advance their agenda. Not what Spain’s government hoped for when they called the election.