Modelling Voter Switching Behavior in a Multiparty System

ABSTRACT - A model of voter choice behavior is presented and applied. Originally the model was developed for analyzing brand choice behavior. Ile model is capable of characterizing the volatility in voter choice behavior overtime. The main advantage of this model is its ability to identify mixtures of volatile and loyal behavior from more simple types of behavior. The model is applied to data from a voting intentions panel, describing voters' intentions over time to vote for political parties eligible for election to the Danish Parliament. The results show that voters appear to be loyal in their behavior towards political parties, but also that many voters appear to exhibit complex behavior alternating between stable and volatile behaviors.


Hans S. Solgaard (1995) ,"Modelling Voter Switching Behavior in a Multiparty System", in E - European Advances in Consumer Research Volume 2, eds. Flemming Hansen, Provo, UT : Association for Consumer Research, Pages: 304-309.

European Advances in Consumer Research Volume 2, 1995      Pages 304-309


Hans S. Solgaard, Copenhagen Business School

The author would like to thank GfK, Denmark, for providing the data for this study.


A model of voter choice behavior is presented and applied. Originally the model was developed for analyzing brand choice behavior. Ile model is capable of characterizing the volatility in voter choice behavior overtime. The main advantage of this model is its ability to identify mixtures of volatile and loyal behavior from more simple types of behavior. The model is applied to data from a voting intentions panel, describing voters' intentions over time to vote for political parties eligible for election to the Danish Parliament. The results show that voters appear to be loyal in their behavior towards political parties, but also that many voters appear to exhibit complex behavior alternating between stable and volatile behaviors.


Voter choice behavior towards political parties is a much researched topic in the political science literature. Several approaches for predicting and explaining voter choice behavior have been proposed. However, most of the theoretical developments, and a majority of the empirical work in this area originated in the US and the UK, where the systems of electoral politics are atypically simple as compared to the systems in most West European countries. The US and UK systems are thus predominantly two party systems. In complex systems where voters can choose between a relatively large number of parties, it becomes more difficult to operationalize these theories into models that can describe and predict voter behavior.

Defections in a multiparty setting from one's 'own' party may well be much easier than in a two party system by simple virtue of the presence of the many other parties. In a typical West European setting, a socialdemocrat, say, would seem to have fairly close policy alternatives to both the right and left, and so moving away from that party need not entail jumping straight to the conservatives as would be the case in a simple two party system. Empirical studies of voter behavior in multiparty systems, indeed, indicate that a considerable amount of switching takes place among the parties from one election to the next, or from one opinion poll to another, (refer for instance to Butler and Stokes, 1974; Irwin and Dittrich, 1984; Maas et al., 1990; Granberg and Holmberg, 1991; and Solgaard and Schmidt, 1992). In line with this, studies also show that many voters appear to be undecided when asked to state which party they would vote for in a coming election, even though they may have strong feelings for certain political values and ideas.

This volatility or wavering of many voters in multiparty systems may be a complicated phenomenon, reflecting rather different kinds of choice decision behavior. For example there may be voters, who are completely undecided, and who do not have any idea which party to vote for in the coming election. Others may have narrowed the choice, being undecided only between a small group of parties, leaning toward one of them, but definitely not voting for parties outside the group. Still others may have strong preferences for one party, but may be contemplating voting for another party for purely tactical reasons. Conceptually voter volatility in a multiparty system can be compared to the switching behavior of consumers in a multibrand product class. In addition it appears to be a widely accepted assumption that voting and buying is governed by similar behavioral principles, (Crosby and Taylor, 1983; and Himmelweit et. al 1981), so that models and techniques developed for analyzing consumer choice behavior could be an important source of inspiration for modeling voter choice behavior.

This paper considers voter volatility and presents a model of voter choice behavior towards political parties developed from a consumer brand choice model. 'Me model is a statistical model that is capable of characterizing individual voter volatility depending on the voter's history of choice in terms of tendencies to move away from or stay with the party voted for at the last one or more elections or polls. The model is estimated at the individual level, and is based on data from a voter intentions panel, i.e. a representative sample of voters from which voting intentions for political parties are recorded every month, 10 or 11 months a year. Relatively long sequences of choice are needed in order to allow estimation of the model, eliminating the possibility for using data on actual voter choice behavior.

The remainder of the paper is organized as follows. First a model of voter behavior is developed and a procedure for estimating it is outlined. This is followed by a brief description of the context in which voter choice will be analyzed, namely the Danish multi party system, and the data set is introduced. The results are then presented and discussed. The paper concludes with suggestions for future research on dynamic voter behavior.


In the theory of voting, several approaches to the explanation of the vote have been proposed. For the Columbia School of thought associated with the works of Uzarfeld et al. (1948), see also Berelson et al. (1954), long term sociological variables appear as the main determinants of the voting decision. The Michigan School represented by the work of Campbell et al. (1954) stresses the importance of psychological variables, attitudes towards issues and candidates, as well as the sociological background of the voter in explaining voting decisions. In addition and in line with these research traditions a number of consumer behavior approaches have been suggested for explaining and predicting voting behavior, refer to Newman (1981), Newman and Sheth (1985), Nakanishi et al. (1974), Palda (1975), Rothchild (1978), Swinyard and Coney (1978), Chapman and Palda (1984), and Himmelweitetal. (1981). Others have described voters and political parties as rational entities acting in markets in which political favors are exchanged for votes, see Downes (1957), Riker (1962), Ordeshook (1987), and Schram (1992).

Model Framework

It is believed that the same principles guiding involved consumer choice decisions also hold with regard to voting decisions. In line with this it is assumed that choice behavior towards political parties is determined by underlying preferences or utilities.

A party might be envisioned as a multiattributed item, a more illustrative description in this case perhaps is as a portfolio consisting of past activities, positions on current issues, statements of future intentions, and various personalities (candidates) offered for consideration by the voters. An individual voter's utility or preference for a party at a given choice occasion is assumed to be some function, (1) of the sum of the utilities provided by the various elements constituting the portfolio of party offerings, and (2) of lagged party choice. Furthermore it is assumed that a voter at any point in time will have an intention to vote for that party which is perceived to maximize his utility, given a threshold level of utility is reached; otherwise she will have no intention to vote.

Influencing the utility formation process arc, (1) the voter's attitudes towards political parties, and (2) situational considerations. Attitude in turn is based on perceptions of party attributes (or elements) and is hypothesized to be directly influenced by the voter's personal characteristics, by parental influences, by school influences and by other stored information, (Goldberg, 1969, and Shively, 1975), besides the indirect influences of these factors via the voter's beliefs.

The impact of lagged party choice on current choice, it is assumed, will vary across the voters, and will depend on factors such as the importance of differences in party attributes, the degree of fuzziness of the voter's party preferences, the role of significant others (parents, school, etc.), and on situational factors in general.

The propensities of voters to react to changes in the various attributes offered by the parties thus may vary considerably. Looking across time this may give rise to some distinct types of choice behavior. Some voters may be most sensitive to current issues and candidates, and may therefore feel induced to switch among two or more parties in order to maximize perceived utility over time, as issues change and candidates change. Also, the focus or concentration on current issues and candidates may lead to a feeling of satiation, ( "of being fed up"), with the currently favored party, i.e. a kind of disutility with respect to the party. Overtime the perceived utility of the favored party is thus seen as declining for this category of voter, which will be denoted as volatile.

For other voters certain issue areas may be permanently important regardless of what current issues and candidates dominate the political debate in the country. Such voters will probably not feel the need to switch to other parties in order to maximize utility, but will stay with the same party for longer periods as a result of their permanent preoccupations. Perhaps at some time considering voting for another party for purely tactical reasons. The perceived utility of the currently favored party for this category of voters will be seen as constant or increasing overtime. These voters will be denoted as stable, i.e. as core voters for the favored party.

Still many voters may alternate between emphasizing more permanent issues (or values), such as ideology, and current issues and personalities, and hence fluctuate between stable and volatile voting behaviors. Over time the perceived utility for the currently favored party will be seen as increasing and then decreasing. The opposite case of first decreasing and then increasing utility is not expected to be possible, since the decrease in utility probably will result in a switch before the utility derived from the party is perceived as increasing. This behavior will be denoted as hybrid choice behavior.

These tendencies to be more or less loyal toward a party thus indicate that an individual voter's future voting in some ways are influenced by his previous voting history, but also that the role of past voting behavior will vary with the individual voter. It will depend on the emphasis put on the various elements of the party portfolios, and of course on her attitudes towards the parties.

Model specification.

The purpose of this section is to build an individual level statistical model that allows for the different types of voting behavior described above, namely volatile behavior, stable behavior, and hybrid behavior. It is not to build a model that can be used as a diagnostic tool to identify important variables influencing choice behavior, rather the purpose is to develop a model that can be utilized to characterize voting behaviors.

As a starting point we must specify how the effect of the individual voter's past voting should be modelled. There are a variety of ways in which this can be done. Pickles et al. (1984), for instance, assumed a voter's last vote to be most influential, and hence specified a first order choice process in analyzing electoral histories for 671 voters covering three general elections in the UK. In the consumer research area volatile brand choice behavior also have most often been modelled as a first order choice process, refer to Givon (1984), and Kahn et al. (1986). However, following Bawa (1990) the assumption will be made that voting on a given occasion is affected by the choices made after the most recent party switch. Thus choice on occasion t is influenced by the choices made at times t-1, t-2, ..., t-r, where the most recent change of voting intention was recorded on occasion t-r, (r>l). The choice process therefore is assumed to renew itself each time a switch takes place, and this assumption of a 'variable order' process, makes it unnecessary to specify the exact order of the process.

A voter's perceived utility for a party, say i, on the (r+l)st choice occasion after r sequential votes for party i, then may be written as,

U(i|ri)=f(wi, ri), i=1,2,..........,n   (1)

while the perceived utility for party j, (j=i), given ri sequential votes for party i, will be written as,

U(j|ri)=f(wj) (j=i)   (2)

where, wi is the part-worth utility or 'base utility' of party i, and ri denotes the number of consequtive votes for party i made after the last switch. Thus if the current run is of party i, then the utility of party i will be a function of past party choice measured in terms of the length of that run, ri, and of the part-worth utility of that party, wi, as in(l). If on the other hand the current run is of some other party j, the utility of party i will be a function of part-worth utility, wi , only, as in (2). Part-worth utility or 'base utility' for party i is a constant that captures the unique aspects of party i, and could be modelled as a function of the party's attributes, refer to Srinivasan (1979) and Lattin (1987).

The next task consists of specifying a particular form of(l) and (2) that can be utilized for identifying the various types of choice behavior outlined above. A two party framework will be used in the following to specify the model in order to minimize the number of parameters to be estimated, since relatively few observations will be available at the individual level. A specification of the utility function as a quadratic function in the run length will be sufficient to capture the various types of choice behavior, thus

U(i|ri)=wi+bri+c(ri)2 i=1,2,..........n   (3)

U(j|ri)= wj (j=i)   (4)

where wi, b and c are parameters to be estimated from the data, and wi are defined above.

Depending on the values of the parameters b and c this specification can describe the different behaviors outlined above.

(a) Volatile behavior. If b:50 and c!-.0, and at least one of the inequalities is holding strict, a model describing volatile behavior results, where U(i|ri) decreases as a function of ri. An extreme case of volatile behavior is obtained if b=O and c=O, implying zero-order choice behavior, i.e. U(i|ri)= wi.

(b) Stable behavior. If b>0 and c>0, and at least one of the inequalities is holding strict the model describes stable choice behavior, where U(i|ri) is an increasing function of ri.

(c) Hybrid behavior. This is the general case where choices are detennined by a mixture of stable and volatile tendencies, and U(i|ri) is a non monotonic function of ri. This case occur if b>0 and c<0, both inequalities holding strict.

Finally, it will be noted that the transitional run length, say r*, for a voter that exhibit hybrid behavior can be derived from equation (3) once the model parameters have been estimated. r* follows as the first-order condition on equation (3), that is, r*=-b/ 2c.

ne value of r* provides an indication of the relative strength of the stable and volatile tendencies for the voter. The larger the value of r* the greater the strength of the stable tendency relative to the volatile tendency, in the case where b>0, c<0.

To map the utility functions (3) and (4) into choice probabilities the conditional logit model will be applied, refer to McFadden (1974). The conditional probability of choosing party i on the (r+l)st occasion, given ri consecutive choices of party i is given by,

P(i|ri)=exp{U(i|ri)}/Sexp{U(k|ri)}. (5)

and the conditional probability of choosing party j, given ri consecutive choices of party i is given by,

P(j|ri)=exp {U(j|ri)}/Sexp{U(k|ri)}. (6)

It is noted that the conditional probability of choosing a party given a run of ri choices of party i, is a function of the utilities of all the parties. The specification (5) and (6) can be obtained by assuming that the stochastic element of utility for each party is independent and identical extreme value distributed. This model has been widely used in choice modeling, see for instance Guadagni and Little (1983), Solgaard (1984), Lattin (1987), Schram (1992) and Hudson (1995).

Model estimation

The model is estimated using the maximum likelihood method. Standard statistical software, i.e. the SAS procedure LOGIST, was used for the actual estimation, (SAS Institute, 1990). For each voter four sets of parameter estimates was obtained. First the general case, b,c*0, is estimated, followed by three special cases i(i) b*0 and c=O, (ii) b=O and cpO, and (iii) b=O and c=O. The purpose of this is to be able to identify the most parsimonious model. The likelihood ratio test, (Maddala, 1983), is used to identify the best model in pairwise comparisons. (In one case, i.e. the comparison between (i) and (ii) the likelihood ratio test is not applicable, since neither is a special case of the other. The model with the largest likelihood value is then preferred).

Problemsetting and the Data.

The analyses in this paper relates to the period January 1989 to December 1991. During this period eight parties were represented in the Danish parliament. The anglicized names of these parties are from the left to the right: Socialist People's Party, Social Democrats, Radical Liberals, Center Democrats, Christian People's Party, Liberals, Conservatives and Progress Party. Besides these parties several other minor parties, mainly on the socialist side, have earned the right to participate in parliamentary elections. None of these parties, however, have obtained a support in the opinion polls that would give them representation in parliament, (i.e. at least two percent of the vote), during the analysis period. An overview of the Danish political parties arranged into partisan blocks, and showing their voter support as measured by an October 1991 opinion poll is presented in Table l. The positioning of the parties on a socialist/ bourgeois or left/right axis is well established with the exception of the location of the Radical Liberals and the Center Democrats relative to each other between the Social Democrats on the left, and the Liberals and the Conservatives on the right. (Refer to Borre, 1984, for a description of the party system and how it has evolved over time).

The data

The data for this study are drawn from the GfK/OBSERVA Mail Panel a well reputed instrument for opinion polls in Denmark. The size of the panel is 1500 members, constituting a representative sample of Danish voters. Also, the panel is a rotating panel in which about 25% of the members are exchanged each year. The limited membership acts to reduce problems of panel conditioning and panel loss, and the continued introduction of new samples of voters help to maintain an up to date sample of the changing voter population. Each member of the panel receives once a month a four page survey questionnaire regarding their voting intention, and current political and social topics. The questions concerning voting intentions are the same each month,

(a) If parliamentary elections were to be held on xx date, (less than a week ahead), will you vote?

(b) If yes, for which party will you vote? (A list of parties eligible for election to parliament is provided).

(c) If no, please state your reason for not voting. (A list of reasons for not voting is provided).

The data used in the following analyses pertains to 31 opinion polls spanning the period from January 1989 through and including December 1991. Over that period the panel had 2718 members, who voted at least once. Although the opinion polls deal with intentions to vote, it is believed that the polls give a correct picture of voter sentiments at any given time. Thus compared to other opinion polls based on different research designs, (i.e. repeated surveys), the GfK/OBSERVA Mail Panel produces results very similar to those of other polls. Also, compared to actual election results the GfK/OBSERVA poll has done very well over the years since its beginning in 1960, when compared to the other opinion polls. It is therefore believed that these panel data provides a correct picture of voter movements between the parties over time.

The total number of cases 2718 were screened in order to eliminate voters that had,

(a) voted less than 20 times in the period; leaving 1075 cases

(b) changed party two or less times during the period; leaving a sample of 335 voters eligible for analysis.

These screenings were necessary in order to obtain sequences of voting intentions that were sufficiently long and with variation in stated choices to allow statistical estimation of the model. Some voters, however, (about 12% of the final sample of 335) were also eliminated after model estimation, because their parameter estimates turned out to be unreliable. An inspection of the choice sequences for these voters showed that they were voters, who almost always voted for the same party, and therefore had too few observations on the other parties to permit good estimates.




Table 2 shows the distribution of voters across the different types of behavior in the sample of moving voters identified above. A number of interesting findings can be observed in this table. First, a considerable number of voters, 139, in this sample exhibit hybrid behavior, that is a fairly complex type of behavior alternating between being loyal and volatile. A behavior that would be difficult to identify in a more conventional first-order model. The average transitional value, r*, for these voters appear to be almost 6, (r*=5.7), meaningthat itwill take on average 6 'elections' to switch behavior, in this case from stable to more volatile behavior, (si nce b>0, and c<0). Second, only very few voters exhibit purely volatile behavior, and no voters appeared to exhibit zero-order behavior. Finally it is noted that among this sample of moving voters, most voters show stable behavior.

Table 3 shows the distribution of voters by type of choice behavior and most preferred party. Note that included as loyal voters in this table are the voters eliminated by criterion b above. No apparent pattern seems to emerge in the distribution of types of behavior across the parties.

In all, these results indicate a competitive 'market' with a considerable amount of switching going on between the parties overtime, but also a 'market' with seemingly complex and cautious choice behavior. The latter at least as compared to the results reported by Bawa (1990) in his analyses of three fast moving consumer product categories. In these analyses there are a considerable amount of consumers with volatile (variety seeking) and zero-order behaviors. This difference is maybe not surprising, and perhaps suggests that voting indeed is a more involved choice than brand choice.


In this study a model of voter choice behavior originally developed for analyzing brand choice behavior, (Bawa, 1990), has been presented and applied. The model is able to characterize the degree of volatility in voter choice behavior across time. ne main advantage being its ability to differentiate mixtures of stable and volatile behaviors from other more simpler types of behavior. The main results are that voters generally appear to be rather stable in their behavior towards political parties, but also that many voters appear to exhibit complex behavior alternating between stability and volatility. In addition, it can be concluded that past choices clearly affect the outcome of a choice decision on any given occasion. Finally, these results can, of course, not be generalized to the entire Danish voter population, due to the rough elimination procedure applied, but they do shed some light on the variation and complexity in voter choice behavior over time.

An interesting question for future research in this area would be to look further into the complexities of the voting decision. For instance by fully developing the utility measure as a function of party attributes and voter characteristics, and by relating the different types of voting behavior to demographic, socioeconomic and psychographic characteristics of the voters.






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Hans S. Solgaard, Copenhagen Business School


E - European Advances in Consumer Research Volume 2 | 1995

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