Popular breakfast markets, new releases in district libraries, free fitness classes, and self-defense courses for women \u2013 these are just a few examples of projects implemented in recent years as part of Warsaw’s participatory budget. This initiative \u2013 also known internationally as participatory budgeting (PB) \u2013 is a democratic process in which residents decide how to allocate a portion of city or municipal funds to projects they propose.<\/p>\n\n\n\n
The idea of participatory budgeting was born in 1989 in the Brazilian city of Porto Alegre and has since gained worldwide popularity. In Poland, the first participatory budget was introduced in Sopot in 2011. Today, residents of both small and large municipalities across the country benefit from participatory budgeting. As of the end of 2022, 320 municipalities in Poland were implementing participatory budgeting.<\/p>\n\n\n\n
However, the initiative is about more than just money or attractive projects. What matters most is the act of participation itself \u2013 engaging in local community affairs and having a say in shaping what directly affects one\u2019s daily life. For this to be meaningful, the budget must be fair. That involves questions such as the accuracy of vote counting and the systems used to select projects. Thanks to a method developed by mathematicians at the University of Warsaw, cities and municipalities now have a way to implement improvements that better reflect residents’ needs.<\/p>\n\n\n\n
One source of dissatisfaction among some voters has been the vote-counting system. Currently, most participatory budgets in Poland use the so-called majority method, which allocates funding to projects that receive the largest number of votes. While this method may seem democratic \u2013 and is still used in electoral systems in many countries \u2013 it is not fully representative. Only the projects with the highest vote totals are implemented, leaving the preferences of significant portions of residents unaddressed. Consequently, projects important to a subset of the community may not receive any funding.<\/p>\n\n\n\n
A clear example occurred in Warsaw in 2021: 39% of voters decided to allocate 46% of the funds to bicycle infrastructure projects. Meanwhile, 4.5% of voters who supported modernizing the running track at Primary School No. 222 \u2013 a project that would have cost just 3.2% of the total funds \u2013 received no funding at all.<\/p>\n\n\n\n
Thanks to the Method of Equal Shares, developed by Prof. Piotr Skowron and his colleagues at the Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, situations like this can be avoided. If votes were counted proportionally, the 4.5% of voters in the example could receive 4.5% of the entire budget for their chosen projects.<\/p>\n\n\n\n
To illustrate the method, researchers use a metaphor: If ten children are given a twenty-zloty bill and use a majority vote to buy chocolates, those who prefer jelly beans or chips will leave disappointed. However, if the money were divided equally \u2013 two zlotys per child \u2013 the minority who prefer jelly beans (three out of ten) would have six zlotys to buy a shared bag of jelly beans. This is precisely how the Method of Equal Shares works in participatory budgeting.<\/p>\n\n\n\n
From the beginning, the scientists intended their method for practical application. In addition to developing a formula to make participatory budgeting more equitable, they conducted simulations showing the effects of implementing the solution. These analyses, supported by real-world examples, could be presented to decision-making bodies. The results are publicly available, and the scientists are open to collaboration with any institution or municipality interested in using the Method of Equal Shares.<\/p>\n\n\n\n
The first local government to implement it was Wieliczka, a town near Krak\u00f3w known internationally for its historic salt mine. In April 2023, the Method of Equal Shares was used to allocate part of Wieliczka\u2019s participatory budget to ecological projects, in an initiative called the Green Million \u2013 a program dedicated to funding environmentally friendly projects.<\/p>\n\n\n\n
Since then, other municipalities have followed Wieliczka’s example \u2013 both in Poland, such as \u015awiecie (a town in northern Poland), and abroad, including Aarau and Winterthur in Switzerland, and Assen in the Netherlands.<\/p>\n\n\n\n
While Wieliczka applied the method to only a portion of its budget, several Polish municipalities have already adopted the Method of Equal Shares for their entire participatory budgeting process. The city of \u015awiecie was among the pioneers, introducing the method in 2023 and continuing to use it today. More recently, in April 2025, the Pruszk\u00f3w City Council approved its use for the city’s full participatory budget, making Pruszk\u00f3w one of the largest municipalities in Poland to implement the method citywide. It remains to be seen whether Poland\u2019s largest cities, such as Warsaw, Krak\u00f3w, or \u0141\u00f3d\u017a, will follow suit.<\/p>\n\n\n\n
“Pruszk\u00f3w will be the largest participatory budget implemented using the Method of Equal Shares, as approximately PLN 2.2 million is allocated there. This demonstrates a compelling relationship, as initially it was the Pruszk\u00f3w County, but their experience was so positive that the city of Pruszk\u00f3w decided to follow their example and amend its regulations to use a better vote counting method,” says Prof. Piotr Skowron.<\/p>\n\n\n\n
“We devoted significant time moving from developing proportionality theory and proving theorems \u2013 purely theoretical research \u2013 to evaluating this method with real participatory budgeting data and simulations, and finally implementing it. We demonstrated that the process can be carried out from start to finish without unexpected complications. And we managed to implement it \u2013 not us directly, but the local governments that applied the method.”<\/p>\n\n\n\n
It’s virtually impossible to find counterarguments against the widespread implementation of the Method of Equal Shares. Its fairness is mathematically guaranteed, it resists manipulation, and implementation costs are minimal because the way the voters cast their ballots does not change. Researchers have also created a simple online tool that allows anyone to see how election results would differ if the Method of Equal Shares were used (https:\/\/pabulib.org\/).<\/p>\n\n\n\n
Thanks to the Method of Equal Shares, the true spirit of participatory budgeting can be realized. Community members gain a real sense of influence over local projects. Without this, a mature and well-functioning civil society is difficult to achieve.<\/p>\n\n\n\n
“Regardless of whether we examine theoretical studies, data analyses, simulations, or citizen satisfaction surveys, the benefits are clear,” says Prof. Skowron. “Participatory budgeting works because it is local. In national elections, such as a presidential vote, it\u2019s easy to feel like your vote doesn\u2019t matter \u2013 it\u2019s just one out of millions. In a participatory budget, one vote may be just one out of 3,000 residents (in \u015awiecie, for example), but it still has a tangible effect. Thanks to the Method of Equal Shares, many more projects can be funded, and individual votes have a real impact.”<\/p>\n\n\n\n