Approval Voting as a Method of Prediction in Political Votings. Case of Polish Elections

Abstract

Applications of approval voting to political analyses are conducted. Polish 2015 presidential and parliamentary elections are considered. A question regarding voting by approval voting method was included in the voting polls. Experiments deal with polls over representative samples and give a possibility to predict a winner of the second round of presidential elections and those parliamentary coalitions which may be approved by groups of voters supporting the given parties.

Authors are very gratefull to Ariadna poll agency for conducting representative polls and to “Secrets of Politics (“Tajniki Polityki”) Web portal for publishing our analyses.

Appendix: 2015 Parliamentary Poll

In this part of our paper we attempted to apply approval voting to the analysis of parliamentary elections. We asked respondents about their best party and for all parties they approved. They were not asked about coalitions but only their choices. We followed the method of the analysis of the Hesse elections [17, 18]. We established whom supported the respondents who chose a given party. On this basis we tried to predict the coalition they may approve. We also asked our respondents to make choice using the disapproval method. Our results demonstrate that the approval and disapproval method do not coincide although they are mathematically isomorphic. A comparison of the results obtained by these two methods show a margin of a potential electorate of a given party.

2015 Polish parliamentary elections took place in October 2015. The poll was conducted about 2 weeks before elections, by Ariadna poll agency, online, over a representative sample. The main debate between the leaders of parties took place after the poll. This influences slightly the similarity between the poll and results of elections. Eight parties were considered in the elections: Prawo i Sprawiedliwość (Law a nd Justice, PiS), Platforma Obywatelska (Citizen Platform, PO), Kukiz 15, Zjednoczona Lewica (United Left, ZL), Nowoczesna (Modern), Polskie Stronnictwo Ludowe (Polish Peasant Party, PSL), KORWIN, Razem (Together). ZL needed more than 8 % to get into Parliament because it was a coalition. The other parties needed more than 5 %. Results of the poll and of the elections are presented in Table 6.

Table 6. Comparison of results of poll and results of election (Source: Authors’ work)

Let us notice that with the exception of ZL and Razem the results of the poll and the elections are very close. ZL and Razem are two leftist parties. Before the main debate only ZL was recognized by a significant part of society. As a result of the debate one of the leaders of Razem became recognizable and some people decide to vote for this party. As the poll was conducted before the debate, significance of Razem would not be reflected in the results. The sum of percent of votes for both leftist parties is close in the poll and in the elections.

There were some additional questions in the poll. These questions were related to voting methods other than classical majority: approval voting and disapproval method. By disapproval method we mean that respondents choose of which parties they disapprove. The party with the lowest number of such votes wins. Approval and disapproval votings are the same from the mathematical point of view. They are not the same from the psychological point of view what will be demonstrated in data obtained from this poll.

Let us analyze Table 7. In this table the results of voting by all three methods are included with the additional information on the number of votes which neither approve nor disapprove of a given party. These votes form a margin of possible support for the party. Let us note that with exception of PiS, where almost everyone has formed opinion, parties have a large margin. People often neither approve nor disapprove of those parties. The lack of opinion renders the thesis “If I do not approve, I disapprove” false. The total numbers of votes casted to parties are different because some respondents did not answer.

Table 7. Parliamentary elections, 2015. Results of classical, approval and disapproval methods (Source: Authors’ work).

Polls did not demonstrate such an advantage of PiS that would eliminate the necessity of forming a coalition government. Questions about approval voting allow to establish which coalition can be approve of by supporters of a given party. We present which other parties gained the approval of the supporters of each of the four parties which obtained the highest number of votes. The other parties obtained such a small number of votes that it was difficult to distinguish a significant support.

Supporters of PiS approve of Kukiz, ZL and KORWIN. The coalition with Kukiz was considered. Supporters of PO approve of PSL, Nowoczesna and ZL. PO was in parliamentary coalition with PSL at that time. Supporters of ZL approve of PO and PSL. Such coalition was also considered. Supporters of Kukiz approve of KORWIN. There was a plan of a coalition between these parties. So, coalitions which can be found by an analysis of approval voting are the same as the coalitions considered in reality (Figs. 1, 2, 3 and 4).

Fig. 1.

(Source: Authors’ work)

2015 parliamentary elections. Parties approved of by supporters of r PiS

Fig. 2.

(Source: Authors’ work)

2015 parliamentary elections. Parties approved of by supporters of PO

Fig. 3.

(Source: Authors’ work)

2015 parliamentary elections. Parties approved of by supporters of ZL

Fig. 4.

(Source: Authors’ work)

2015 parliamentary elections. Parties approved of by supporters of Kukiz