Anti-government demonstrators set up a large inflatable doll in the likeness of Brazil’s President Dilma Rousseff wearing sashes with “Goodbye dear” and (loosely translated) “The Petrobras scandal is my fault” written in Portugese, in Sao Paulo on May 11. (Andre Penner/AP)

There’s a new twist in the already twisted saga of the Brazilian legislature’s attempt to impeach President Dilma Rousseff, who is currently suspended. On May 23, Brazil’s largest newspaper, the Folha de Sao Paulo, published a story about a leaked conversation between Planning Minister Romero Jucá — a key instigator of Rousseff’s suspension and an important political insider for the past 30 years — and Sérgio Machado, the former head of Transpetro (the transportation arm of Petrobras, Brazil’s state-owned oil company).

In the audio clip, Jucá — who has since taken leave from his post in Michel Temer’s interim government, which stepped in for Rousseff — says clearly that impeachment was a way for a coalition of politicians to avoid being prosecuted for corruption. Rousseff was unwilling to protect these politicians, Jucá claimed. Removing her from office and forming a “national pact” to “stop the bleeding” would be the best way for them all to protect themselves.

Some media outlets suggest that Machado recorded conversations with other key players in Brazilian politics. If so, more leaks could put Temer in a still worse position. Temer worked actively behind the scenes to dethrone his predecessor, but doesn’t have popular support himself.

Corruption — and leaked conversations — are at the center of the political crisis now paralyzing Brazil. But how did we get here? A large part of the explanation rests with Brazil’s electoral rules and party system.

Brazil’s political system is a hybrid of two very different democratic approaches

The nation’s executives and senators are elected through a presidential system: presidents, governors and mayors win by majority run-off, while senators are elected by a plurality of the vote. But the lower house looks more like a parliamentary system. Lower house deputies are elected in proportion to the votes that their parties receive across the country, in what political scientists call a proportional representation, or PR, system.

But unlike the more common parliamentary or closed-list proportional representation systems, parties in Brazil do not decide who wins the seats that the party is allocated. While seats are awarded in proportion to the votes that each coalition wins, it is a straight-up popularity contest from there on in: The candidates who win seats are those who win the most votes within each coalition. Furthermore, each of Brazil’s 27 states serves as a giant electoral district, including Amazonas, which is more than twice the size of Texas, and Sao Paulo, a state with more than 44 million people.

So to get elected, candidates for deputy need votes not just for their party, but specifically for themselves. They need to find ways to stand out among thousands of other candidates in dozens of other parties potentially vying for an electoral district with up to 32 million voters.

You can imagine how difficult that is. Voters in two-party systems such as that of the United States have difficulties remembering the policy differences between two candidates running for one office. Distinguishing among thousands can be nearly impossible. Consider that, while voting for a deputy in 2014 in the state of Sao Paulo, fully 20 percent of the electorate spoiled the ballot, abstained or made a mistake. To put it mildly, it’s not easy to win an election in Brazil.

How do you win more votes than thousands of other candidates?

To get votes, a candidate must stand out from the crowd. Some do that by recording a zany campaign advertisement, perhaps even in costume. Another, more common, tactic is to slip voters a 50- or 100-real bill (equivalent to about $14 and $28, respectively) along with the campaign literature. Doing this across an entire state, however, requires a lot of money.

Big companies are often happy to help — and could do so legally until 2015, when Brazil’s Supreme Court ruled that only the government and individuals could fund campaigns. But companies do not select specific parties to support. Instead, they treat their donations as investments, doing what all smart investors do: diversifying. In other words, they pay almost every candidate, regardless of party or whether the contribution is legal.

But of course, these companies want something in return: government contracts. They expect that, when in office, the politicians in whom they have invested will “help” them win government contracts. To seal the deal, they include a sweetener — a kickback that either finds its way into the politician’s campaign coffers or offshore bank accounts.

In other words, politicians and elected officials have strong incentives both to accept money under the table and distribute public resources under the table.

Weak parties proliferate, but what matters are the cross-party caucuses

Given the expense of running, most politicians are always looking for campaign funds, but their parties can’t afford to help much. As a result, many politicians — particularly those with low national profiles (often referred to as the “baixo clero,” or “the lower clergy”) — change parties like they were clothes, searching for the highest bidder.

And they have plenty of options. Brazil currently has 35 political parties, 25 of which have representatives in the lower house. In fact, as one of us did field research in Brazil, he noticed that many candidates could not even remember who was in their coalitions. Nobody can be a candidate without being affiliated with a political party, but that party affiliation is often just a formality.

In fact, parties can take a back seat to bancadas suprapartidárias, or supra-party Congressional caucuses. These caucuses are formed by interest groups. Powerful caucuses — like the rural, evangelical and labor union caucuses — often command more loyalty than political parties. They can be true alliances of economic interest, further dividing the loyalties of the 594 members of Congress.

With this confusing system, how do you pass legislation?

Now let’s add up all those elements: politicians perpetually searching for funds; parties that lack organization or power; and powerful interests that cut across party lines. Getting a law passed involves forming a voting coalition of hundreds of individuals from more than a dozen parties.

One way to do this is simple: Pay deputies and senators, as members of Lula’s government did during the last decade. Yet more recent investigations by the Federal Police have uncovered new, far bigger schemes, indicating that last decade’s Mensalão scandal was just the tip of the iceberg. To move the wheels of government, you have to pay individual members of Congress. Without that grease, Congress grinds to a halt — which is precisely what has happened over the past year.

The renowned Italian political scientist Giovanni Sartori once wrote that presidential systems with many political parties would be recipes for political crisis. Brazil seems to be a case in point.

Was this a crisis waiting to happen?

With so much disorganization, dealing with Congress is essentially like herding cats. This particular Congress is not only fragmented but also notably conservative. That never boded well for a left-of-center government like Rousseff’s.

So it may be no surprise that once the Federal Police began to knock on doors, looking for people who had taken illegal campaign funds, many in Congress would panic. When Rousseff refused to shelter key allies from prosecution, they began to organize the mutiny. After all, if there’s one thing members of Congress can agree on, it is that they would not like to be thrown in jail.

Brazil’s democracy is only 28 years old, still maturing and improving. Yet it has found itself in a very difficult situation. Much of the blame lies on the electoral and party systems. Perhaps the surprise should not be that Brazil has arrived at this point, but rather that it has taken so long to do so.

Ryan Lloyd is a PhD candidate at the University of Texas at Austin and a junior collaborating researcher at the University of Brasília.

Carlos Oliveira is a PhD student at the Political Science Institute (IPOL) at the University of Brasília and a journalist with extensive experience covering the Brazilian Congress.