IS APPROVAL VOTING PREFERED BY THE POLISH SOCIETY? OBSERVATIONS FROM A REPRESENTATIVE SAMPLE 1

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1 IS APPROVAL VOTING PREFERED BY THE POLISH SOCIETY? OBSERVATIONS FROM A REPRESENTATIVE SAMPLE 1 Krzysztof Przybyszewski Center for Economic Psychology and Decision Sciences, LKAEM, Warsaw, Poland crispy@wspiz.edu.pl Honorata Sosnowska 2 Center for Economic Psychology and Decision Sciences, LKAEM, Warsaw, Poland and Warsaw School of Economics, Warsaw, Poland honorata@sgh.waw.pl 1 Introduction Under approval voting, voters vote for as many candidates as they wish to. For example, consider a situation where there are many candidates for a single position. Voters have a list of candidates and mark these candidates which they approve for this position. They can approve one candidate, more then one or even none. The candidate who is marked the most number of times by the society wins. This system was proposed independently by many in the 70s. Theoretical presentation and analysis was done by Brams and Fishburn in their book Approval voting (1982). Approval voting is applied in many cases, for example in scientific societies and even at the Security Council of the United Nations. There are many different opinions about advantages of approval voting. In particular, approval voting may be considered as a voting system in presidential elections with many candidates. Laslier and van der Straeten conducted research during the This research was partly sponsored and conducted in cooperation with poll agency TNS OBOP 2 This author will present the paper 1

2 French presidential elections based on exit poll on some voting posts in two towns. However, they did not use a representative sample. In our research we study the 2005 Polish presidential elections. We conducted pre-election poll on a representative sample before the presidential elections. The poll was conducted by the polling agency TNS OBOP. We asked questions about candidates and about participation in elections. It is well known that winners in approval voting may be different from winners in standard systems. There was also the question whether participation in elections in a case in approval voting may be different than in a case of standard voting. Some people may prefer approval voting because they do not know whom to choose and it is easier for them to mark more candidates. On the other hand some may find it more difficult to face the possibility of marking more than one candidate and consider approval voting as a more difficult system than a standard one. We think that if people declare higher voter turnout in case of approval voting than in a standard system, then they prefer approval voting. Otherwise, they prefer the standard system. 2 Polish parliamentary elections and the poll Polish parliamentary elections have two rounds. In the first round voters vote for candidates in the majority system. A candidate wins if he gets more than 50% votes. Otherwise, the second round of voting takes place. There are two candidates in the second round. They are the candidates who got the two highest numbers of votes in the first round. Polish parliamentary elections took place in the beginning of October, The poll was conducted during September, 8-12, It was about 4 weeks before the elections. There were 15 candidates. One of them, Włodzimierz Cimoszewicz cancelled his candidature before the election, but after the poll. Cimoszewicz was a quite popular candidate, so the results of the poll are not deformed by his absence. None of candidates got majority in the first round. Donald Tusk won the first round. He and Lech Kaczyński moved as canditates in the second round. Kaczyński won the second round and became the president. The poll was conducted over the representative sample of 1005 Poles, aged 15 or more years. Pollsters asked people four questions. First they were asked whether they would participate in elections. Then, they chose the candidate by majority rule. Next, the approval voting system was presented and people chose their candidates by approval voting. The last question concerned the participation in elections if they would be conducted by approval voting. People also filled a standard questionnaire with questions about age, sex, education, occupation and so on. 3 Results (i) Influence of the voting system on results of elections The following table presents the results of both voting for first 5 candidates. The only difference is between Borowski and Lepper (4th and 5th position). 2

3 L.P CANDIDATE APPROVAL VOTING MAJORITY METHOD 1. Tusk Kaczyński Cimoszewicz Borowski Lepper Table 1. Results of voting The complete results of both voting are presented in the following diagram. Let us consider Donald Tusk. He won in both cases, but his advantage was smaller in case of approval voting. So, if Tusk was treated as one of possible candidates (approval voting) he got a worse result than in a situation where he was a definite candidate (majority voting). Tusk lost in the second round,where voters chose between candidates who were not their best ones. 45,00% 40,00% 35,00% 30,00% 25,00% 20,00% 15,00% 10,00% 5,00% 0,00% 4,18% 2,43% 0,43% 9,80% 0,14% 0,25% 16,57% 13,74% 3,31% 4,36% 0,29% 0,84% 22,33% 21,78% 7,49% 7,71% 4,36% 2,45% 0,72% 2,18% 0,29% 0,17% 41,07% 31,07% majority approval 0,72% 1,09% 0,00% 0,17% 0,00% 0,08% Henryka Bo chniar Marek Borowsk Les zek Bub e W łodz im ierz C im osz ew Maciej Giertyc Liwiusz Ilasz Lech Kaczyńsk Jarosła w Kalinows Janusz Korwin -Mikk And rz ej L eppe Ada m Słom k Donald Tus Sta nisław Tym ińs Daniel P odrzyc Jan Pyszko Diagram 1. Full results of elections. (i) Declared participation in elections Voters were asked to declare their participation in elections where the standard majority method would be used vis a vis the case of approval voting. We use the following scale for declarations of participation. Grade 1 - person is sure that he will not participate in the elections, 2 - person thinks that he would rather not participate, 3 - person does not know whether she would participate, 4 - person thinks that she would rather participate, 5 - person is sure that she will participate. Majority voting got 3.96, approval voting The majority method has advantage over approval voting. So, it may be interpreted that Polish society prefers standard majority rule than approval voting. More detailed analysis shows that the declared participation was connected with education. More educated people more frequently 3

4 declared participation in elections and approval voting was more accepted by highly educated voters. The advantage of majority method was made by the fact that in case of approval voting more people chose the answer I do not know whether I shall participate in elections. Voters voted independent of their declaration about participation in elections. There was a very small difference between numbers of people voting in both methods. 694 voters voted in case of majority method and 669 voters voted by approval voting. Voters used the possibilities of multiplied choice in approval voting in the following way. 269 voters chose 1 candidate, 288 voters chose 2 candidates, 99 voters chose 3 candidates, 13 voters chose 4 candidates. None chose more than 4 candidates. (ii) Hidden electorate In a situation of two rounds of elections most voters do not vote on their best candidate in the second round. We tried to predict voters preferences in the second round by analysis of the advantage coefficients. Advantage coefficient of candidate x over candidate y is computed as a quotient number of votes on candidate x is divided by number of votes on candidate y. The following table presents advantage coefficients for the candidates. Number x/y is in the column of candidate x and in the row of candidate y. Star denotes the majority method, blue approval voting. TUSK KACZYŃSKI LEPPER CIMOSZE BOROWSKI 285* * * * * 117 TUSK 285* 0,53* 0,18* 0,40* 0,10* 371 0,71 0,25 0,44 0,32 KACZYŃSKI 151* 1,89* 0,34* 0,76* 0,19* 265 1,40 0,35 0,62 0,44 LEPPER 52* 5,48* 2,90* 2,21* 0,56* 92 4,03 2,88 1,78 1,27 CIMOSZEWICZ 115* 2,48* 1,31* 0,45* 0,25* 164 2,26 1,62 0,56 0,71 BOROWSKI 29* 9,83* 5,21* 1,79* 3,97* 117 3,17 2,26 0,79 1,40 Table 2. Advantage coefficients (star- majority voting) Notice that Tusk s advantage coefficients are lower in the case of approval voting than in the case of majority voting. Kaczyński s advantage coefficients are higher in the case of approval voting than in the case of majority voting. It may then be argued that Kaczyński had a socalled hidden electorate, that is, voters who approve him as a president do not consider him as the best candidate. Kaczyński won the second round, Tusk lost. In the most traditional polls, which were conducted that time, Tusk was ranked before Kaczyński. Tusk s negative electorate was also considerably lower. References S.J. Brams, P.C. Fisburn, (1982), Approval Voting, Birkhäuser, Boston J.F. Laslier, K.Van dre Straeten, (2004), Vote par assestiment pendant la presidentiele de 2002: analyse d une expérience in Française de Science Politique 54, pp Extended abstract Approval Voting: An Experiment During the French

5 Electoral Competition in Logic, Games and Social Choice. Proceedings of the International Conference LGS3, ed.s. Vannuci, Siena University Press 2003, pp Krzysztof Przybyszywski, Honorata Sosnowska, Frekwencja w głosowaniu aprobującym. Raport końcowy (Final report on voter turnout in a case of approval voting), LKAEM, Warsaw, 2005, manuscript 5