Estimating party-user similarity in Voting Advice Applications using Hidden Markov Models

Abstract

Voting Advice Applications (VAAs) are Web tools that inform citizens about the political stances of parties (and/or candidates) that participate in upcoming elections. The traditional process that they follow is to call the users and the parties to state their position in a set of policy statements, usually grouped into meaningful categories (e.g., external policy, economy, society, etc). Having the aforementioned information, VAA can provide recommendation to users regarding the proximity/distance that a user has to each participating party. A social recommendation approach of VAAs (so-called SVAAs) calculates the closeness between each party's devoted users and the current user and ranks parties according the estimated `party users' - user similarity. In our paper we stand on this approach and we assume that `typical' voters of particular parties can be characterized by answer patterns (sequences of choices for all policy statements included in the VAA) and that the answer choice in each policy statement can be `predicted' from previous answer choices. Thus, we resort to Hidden Markov Models (HMMs), which are proved to be e ective machine learning tools for sequential and correlated data. Based on the principles of collaborative ltering we try to model `party users' using HMMs and then exploit these models to recommend each VAA user the party whose model best ts their answer pattern. For our experiments we use three datasets based on the 2014 elections to the European Parliament1.

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Hidden Markov Models; Voting Advice Applications; collaborative ltering; expectation maximization; recommender systems

1. INTRODUCTION

Citizens, partly because of their lack of knowledge on the political issues, tend to avoid the democratic decision making process contributing in low voter turnout that a ects the most advanced democracies. Ladner and Pianzola [ 18 ] speci cally mentioned Switzerland, where the voter turnout does not exceed 50% by 1975. E-democracy tools and services can be used to inform people about the political stances of the parties (and/or candidates) who take part in the upcoming elections, aiming at increasing citizen participation and promoting direct involvement in political activities [ 22 ]. Voting Advice Applications (VAAs) are speci cally designed e-democracy tools that further serve this purpose [ 17, 26 ]. They have been applied to facilitate citizens' decision making process by matching their political stances with those of parties and/or candidates. Findings have shown that VAAs' recommendations a ect the decision making process of a signi cant part of voters, especially those who are undecided or belong to speci c categories, such as people under 34 years old and/or rst time voters [ 9, 26 ].

Recommender Systems (RSs) are software tools and techniques, which recommend products or services to users, in an e ort to help them decide what they really need from the sheer volume of data that many modern online applications manage [ 14, 24 ]. Although the recommender systems are strongly a liated with the eld of e-marketing, several other application areas were also emerged. Recently, several researchers used recommender systems for e-elections in e-government to inform citizens about candidates and enhance their participation in democratic processes [ 7, 28 ], while Katakis et al. [ 15 ] introduced SVAAs (Social Voting Advice Applications), an extended form of VAAs that is based on the principles of collaborative ltering.

VAAs ask users and parties to ll a speci c questionnaire that contains a number of policy statements, which are selected according to issues that concern the nation in time of elections and represent important political, economic and social issues [ 15, 19 ]. Figure 1 shows an example of such a policy statement along with the set of possible answers a user can select. The recommendation process that a VAA traditionally follows contains two main steps: rst, it calculates the similarity scores utilizing the user's and the parties' and/or candidates' answers in the policy statements and then, the VAA ranks the parties according to partyuser `similarity'. Figure 2 presents an example taken from the German VAA of the elections to the European parliament in 2014.

Researchers from di erent research elds deal with many aspects of VAAs [ 25 ]. Some of them investigate whether VAAs urge citizens to vote and whether recommendations made by these systems a ect the nal vote decision [ 9, 26 ]. Other researchers are interested in the design of VAAs dealing with practical issues such as the derivation of optimal party-user similarity estimation methods that accurately predict users' voting intention [ 20, 21, 29 ]. We note here that the estimation of similarity between users based on their choices from a set of products is a core problem in Recommender Systems as well.

Recently Katakis et al. [ 15 ] coined the term `Social VAAs' (SVAAs) in an e ort to describe VAAs, whose recommendation is based on the collaborative ltering philosophy that is widely used in RSs [ 12, 13 ]. SVAAs in addition to parties' answers to the policy statements, they also utilize models that capture the behavior - in respect to the policy statements - of each party voters. Thus, a social VAA has the same policy questionnaire with the traditional VAA but also party voters models created by estimating the joint probability of answer patterns and vote intention of each user. Vote intention is an opt in question which is included in VAAs as one of the supplementary questions. An example of supplementary questions included in VAAs is shown in Figure 3, where the vote intention question is the second one.

In SVAAs users are classi ed into groups according to their voting intention, i.e., party or candidate choice, and then models are created for each party to 'show' the common way, if any, in which party supporters ll the online questionnaire producing their own answer pattern. Then, the SVAA recommends new user with the party or the candidate whose users' model matches better their answer patterns. Figure 4 presents an example of the matching scores presented to a user based on the SVAA philosophy. SVAAs proved to make better voting predictions than the traditional matching schemes between users' and parties' proles [ 1 ]. In addition, as recorded by users' feedback through the emoticons shown in the right part of Figures 2 and 4, SVAA recommendation surpasses VAA recommendation in terms of users satisfaction [ 6 ].

In order to tackle the recommendation problem of SVAAs, machine learning techniques [ 2 ] can be used to indicate the likelihood that a user belongs into a class, where each class corresponds to a speci c party. In essence, what is accomplished with machine learning is to model each party cording to its supporters' answer patterns to policy statements. Thus, if a user is classi ed into a party, it is more likely this user has the same political positions with people who are already classi ed to the same party. Katakis et al. [ 15 ] resorted to clustering and classi cation approaches for generating vote advice in SVAAs and they showed that party voter modeling based on data mining classi ers and Support Vector Machines, achieve the best performance.

Tsapatsoulis and Mendez [ 30 ] dealt with building party voter models for SVAAs based on the probability to vote each one of parties participating in the German elections in 2013. They compared a Mahalanobis Classi er, a Weighted Mahalanobis Classi er and function approximation approaches, and they concluded that there is no much gain when using the probability to vote instead of the vote intention. They also noticed that non-linear party modeling techniques, such as neural network based ones, outperform the linear methods like Mahalanobis.

Tsapatsoulis et al. [ 29 ] in an e ort to provide practical design guidelines for SVAAs dealt with the problem of nding the minimum number of VAA users required to build e ective party's voter models. They limited their analysis to the Mahalanobis Classi er for minimize the factors inuencing their research questions. They found that, as the number of parties modeled is increased the performance of recommendation is decreased. In addition they showed that e ective party voter models can be built based on a rather small number of user pro les.

In this work we adopt the social approach of VAAs and we investigate the application of Hidden Markov Model (HMM) classi ers for party-user similarity estimation in an e ort to improve the e ectiveness of social vote recommendation. HMM classi ers provide a way to apply machine learning to data represented as a sequence of correlated observations [ 2 ].

In VAAs the order in which policy statements are displayed to users is not important; however, policy statements are usually correlated and grouped into categories (e.g., external policy, economy, society, etc). Thus, opting from the various answer choices in each policy statement is related with selections in previous and subsequent policy statements. Given that the order of policy statements is kept xed within each VAA one can assume that (a) answer patterns, that are sequences of choices for all policy statements included in the VAA that characterize `typical' voters of particular parties can be found, and (b) the answer choice in each policy statement can be `predicted' from previous answer choices. When users answer the questions, they are incrementally producing a sequence of symbols. Whenever a process includes a sequence of dependent observations, HMM classi ers can be used to model input sequences as generated by a parametric random process. This is our basic rationale for employing HMMs for obtaining similarity matching between parties and users for SVAAs.

We assume that VAA users, who support the same party, produce similar sequences of symbols, i.e., answer patterns. Thus, HMM classi ers can be used to predict and identify the `path' that users, who support the same party, follow to answer the online questionnaire, and to create simple and compact models for each party, so as to be able to classify new users into the most probable party class. Although there is enough evidence about the appropriateness of HMM classi ers for SVAA recommendation, they have not been applied so far. This is probably due to the fact that there are simpler machine learning techniques that can be used instead. However, we strongly believe that HMMs have an ad(1) (2) vantage compared to other machine learning methods: they can capture the correlation between answers in di erent policy statements.

In short, the purpose of our paper is to introduce an SVAA method for similarity matching between parties and users based on HMMs and investigate its performance based on the accuracy of predicting their voting intention. We show that, even if the order in which the questions are answered in a VAA does not really matter, the HMM classi er performs quite well in estimating vote intention of unseen users. Nevertheless, the HMMs' performance relies on the smooth distribution of samples per party and on the consistency between the answers of the users, who are classi ed as belonging to these parties. Therefore in the cases where these conditions are not met, the results may not be satisfactory; in such case datasets used for training should be cleaned using outlier and/or rogue detection techniques [ 5 ].

To the best of our knowledge this is the rst time HMMs are used to compute party-user similarity either in VAAs or in SVAAs. For our experiments we use three datasets derived from EUVox 2014. EUVox is an online application that was sponsored by the Open Society Initiative for Europe (European Elections 2014) and the Directorate-General for Communication of the European Parliament (area of internet-based activities/online media a^AS 2014). It purpose was to help voters to have quick access to information related to the political positions of the parties participated in the 2014 elections to the European Parliament (see more information at http://www.euvox2014.eu/). The chosen datasets di er in size, in the number of parties participating in the elections and in the population's distribution percentage among the various parties. An important, possible, contribution to researchers belonging to the Recommender Systems community is that the corresponding datasets, as well as many other VAA datasets, are freely available through the Preference Matcher Website2. One of the aims of the current work is to mobilize researchers of RSs to investigate the performance of their techniques on VAA data. 2.

PROBLEM FORMULATION

The basic aim of a traditional VAA is to recommend parties to users. In such a case there is a set of N users X = fx~1; x~2; : : : ; x~N g, a set of U policy statements Q = fq1; q2; : : : ; qU g, and a set of D political parties or candidates P = fp~1; p~2; : : : ; p~Dg. Each user ~xj 2 X and each political party p~i 2 P , has answered each policy question qk 2 Q.

Based on their answers, every political party or user can be represented in a vector space model: ~xj = fx(j;1); x(j:2); : : : ; x(j;k); : : : ; x(j;U)g p~i = fp(i;1); p(i;2); : : : ; p(i;k); : : : ; p(i;U)g where x(j;k); p(i;k) 2 L are the answers of the j-th user and i-th party, respectively, to the k-th question. The vectors ~xj and p~i are, usually, named user and party pro les respectively.

A typical set of answers is a 6-point Likert scale: L =f1 (Completely disagree), 2 (Disagree), 3 (Neither agree nor 2http://www.preferencematcher.org/?page id=18 disagree), 4 (Agree), 5 (Completely agree), 6 (No opinion)g. In several cases, and in the majority of SVAA methods proposed so far, the sixth point is not taken into consideration since it does not correspond to a particular stance and is usually replaced with the third point, i.e., with `neither agree nor disagree'. In this work we decided to keep the sixth point as a distinct emission symbol (see also Section 3) in order to avoid a common criticism by political scientists who strongly argue about the di erence between these two categories [ 3 ]. As a result the set L, in the context of this study, becomes: L =f1,2,3,4,5,6g. Figure 1 shows an example of the way the policy statements in the EUVox 2014 appear and how the answer options are presented to VAA users.

The VAA recommendation task tries to approximate the unknown relevance h(j; i) of user j to party i given the user's answers x~j and then to suggest a ranking of political parties based on user-party similarity. In machine learning terms, the task is to approximate the hidden function h(j; i) with a function h^ : RU RU ! R, where h^(~xj ; p~i) is the estimation of the relevance of user j with political party i. Typically h^(~x; p~) 2 [0; 1]. In each case, the top suggestion pjq for user j should be: pjq = argmax(h^(x~j ; p~i)) | {z } i (3)

In many VAAs, the users are asked to answer a number of supplementary questions in addition to the U policy statements. One of these supplementary (opt in) questions is the vote intention of user i.e., which party the user intends to vote in the upcoming election. An example of the type of supplementary questions and how they appear in the EUVox 2014 is shown in Figure 3.

The main idea behind the SVAA is to use the vote intention variable yj and model each party's voters using statistical or machine learning approaches. Thus, for every party i a model M~ i is created using as training examples the subset Ti of user pro les who expressed voting intention for party i, that is Ti = [~xj jyj =i]. Then, these models can be exploited to provide a recommendation based on collaborative ltering [ 11 ] that takes advantage of a VAA's voter community. In this case the top recommendation pjq for user j is given by: pjq = argmax(h^(x~j ; M~ i)) | {z }

i In this work we use Hidden Markov Models to create the ~ party-voter models Mi (see Section 3). Thus, Eq. 4 becomes: pjq = argmax(h^(V j ; i)) | {z }

i where V j is the set of observations corresponding to user pro le x~j and i is the party-voters model for party i created using HMM training. The solution of Eq. 5 is obtained with the aid of Viterbi algorithm as usually happens in HMM classi ers [ 2 ].

An HMM is a double stochastic process that models data evolving in time. It is de ned by a latent Markov chain, which consists of a nite number of states, and a number of observation probability distributions for each state. At each (4) (5) discrete time instant, the system switches from one state to another, while an observation is produced by the probability distribution according to the current state [ 16 ]. In an HMM, the states are not observable, i.e., they are `hidden', but an observation is generated as a probabilistic function of the state, when the system visits the state [ 2 ].

An HMM is described by three parameters: = (A; B; ), which can be estimated based on specialized Expectation Maximization (EM) techniques, such as the Viterbi or the Baum-Welch algorithm. The parameters are calculated through several training iterations, by using the entire training data set at each time, until an objective function is maximized. To avoid knowledge corruption, the data should be storage in memory and be trained from the start at each iteration, a costly and time consuming process. Therefore in real life, the datasets used for training HMMs are often small and this might signi cantly reduce their performance since the e ectiveness of HMMs depend heavily on the availability of a su cient quantity of representative training data to calculate the model parameters [ 16 ].

As already stated, in this work we try to optimize SVAA recommendation with the aid of a Hidden Markov Model classi er. This is, probably, the rst time the HMMs are used in SVAAs and one of the very few times used in Recommender System applications in general. A possible explanation is the fact that within a VAA, and in many RSs, the observations corresponding to user (answer) choices are not time dependent. However, as we already mentioned, in VAAs user answer choices can be considered as a sequence of correlated observations while HMM states could correspond to the set of permissible answer options (`Completely disagree', `Disagree', `Neither agree nor disagree', `Agree', `Completely agree'). Under these circumstances the HMMs can be applied to VAA, as we have a su cient number of states and a fairly rich set of data. 3.

METHODOLOGY

An HMM is characterized by [ 2 ]:

A set of W discrete states S = S1; S2; S3; :::; SW , with G = g1g2:::gT to be the state sequence (i.e., if we have gt = Si that means at time t the system is in state Si). A set of E observations V = v1; v2; v3; :::; vE, with O = O1O2:::OT to be the sequence of observations corresponding to states G.

A state transition matrix A, that shows the probability of going from state Si to state Sj : A [aij ] where aij P (gt+1 = Sj jgt = Si).

An observation emission matrix B, that describes the probability of observing ve in state Sj : B [bj (e)] where bj (e) P (Ot = vejgt = Sj ).

The probability distribution of being in the rst state of a sequence: [ i] where i P (g1 = Si).

In our implementation we consider HMMs with three states, i.e., W = 3, S = fS1; S2; S3g, labeled as S1: `Negative', S2: `Neutral', and S3: `Positive' corresponding to answer choices S1: (Completely disagree, Disagree), S2: (Neither agree nor disagree, I have no opinion), and S3: (Agree, Completely agree) that could be given in the U policy statements of the VAA questionnaire. Furthermore, there are six possible observations V = fv1; v2; v3; v4; v5; v6g, where v1: `Completely disagree', v2: `Disagree' v3: `Neither agree nor disagree', v4: `I have no opinion', v5: `Agree', and v6: `Completely agree'.

Every state sequence G has length equal to the number of policy statements, i.e., T = U = 30 while the mapping from a user pro le x~j (see also Eq. 1) to an emission sequence V j = fv1; v2; v3; :::; vEjg is obtained as follows: j j j vqj = x(j;q) + jLj (q 1) (6) where x(j;q) is the answer choice of user j to policy statement q (q = 1; :::; E), L is the set of answer options (see also Section 2) and jLj is its cardinality, i.e., the number of answer options in the policy statements. Thus, in our case jLj = 6.

As an example consider that a VAA user selected `Completely Disagree' in the 1st policy statement; then, according to Eq. 6 the recorded observation in the 1st place of the sequential answers of the voter would be: 1 + 6 (1 1) = 1; whereas if the answer choice in the 23rd policy statement was `I agree', then the observation 4 + 6 (23 1) = 136 would be registered in the 23rd place of the V j sequence.

An HMM is fully described by three parameters: = (A; B; ). In the framework of this work we consider that each party voters can be modeled by an HMM i since the way VAA users respond to the rst policy statement di ers among supporters of di erent parties re ecting into di erent i, the same holds for any other policy statement re ecting in di erent Bi, while the way answer choices are given in two consecutive policy statements also varies among di erent party supporters re ecting into di erent Ai.

Datasets

EXPERIMENTAL RESULTS

As in the majority of VAA and SVAA methods, in this work we set the performance criterion to be the accuracy of predicting a user's vote intention. This also aligns with the approach followed in Recommender Systems where the criterion is the accuracy of predicting users' ratings. Thus, we carried out experiments to measure the performance of voting prediction by applying the HMM classi er on three EUVox datasets derived from Denmark, Bulgaria and Czech Republic. EUVox is an EU-wide voting advice application that was utilized during the 2014 European Parliament elections. Its questionnaire consists of 30 policy statements and it is based on European-wide issues, issues that are salient for voters in a particular region, and country-speci c issues. The policy statements are clustered into three groups; to those that refer to European Union issues, to those dealing with economy, and to those related to societal issues.

The three datasets were chosen such as to di er in size. The number of samples of the Bulgarian dataset is quite small; approximately 2800 entries were correct and also contained a voting intention answer. The Czech dataset is approximately 5 times larger than the Bulgarian while the Danish dataset is the largest; it contains almost 4 times more samples than the Czech dataset. In addition the number of parties participating in the elections varies among the selected datasets while the same holds for the population distribution among the various parties. The Danish dataset is characterized by a rather smooth distribution of samples per party which is not the case in the Bulgarian and Czech datasets (see Figure 5). These di erences helped us to examine the behavior of HMMs when there is no su cient number of data points per party and when the number of samples varies among parties.

In order to measure the performance of voting prediction using HMMs, we took into consideration only the users who expressed a voting intention for a speci c party. Therefore, the questionnaires of the users, who did not answer the supplementary question on voting intention, or answered either `not decided yet' or `I will not vote' were exempted. In all three datasets approximately 40% of the VAA users expressed voting intention for a speci c party. The main characteristics of the used datasets are summarized in Table 1. 4.2

Results and Discussion

Experiments were designed to investigate the performance of social voting recommendation using HMMs for estimating party-user similarity. For the evaluation we divided the users of dataset into a training and a test set [ 8 ]. A HMM is built against the training set Tr = f(~xj; yj)jj = 1:::Nl; yj 6= ;g consisting of the pro le vectors ~xj corresponding to user answers to the online questionnaire along with the user's expressed vote intention yj. Evaluation of the trained HMMs on unseen data was facilitated using the test set Te = f(~xt; yt)j(~xt; yt) 2= Tr; t = 1:::Nt; yt 6= ;g which is a set of pro les and voting intention pairs (~xt, yt) not used in the training set.

In order to perform our experiments we resorted to Matlab's HMM toolbox. This toolbox was built by Kevin Murphy and it uses the Baum-Welch (BW) algorithm for estimating the parameters of HMMs with discrete outputs [ 23 ]. We created an HMM i = (Ai; Bi; i), for every party included in each one of the datasets. Thus, we ended up with seven HMMs for the Danish and Bulgarian datasets and ten models for the Czech dataset. After training the party models using the training set Tr the test set Te was used to classify unseen users, expressed through their pro les, into the party in which the user most likely belongs to, i.e., the user's answer pattern most accurately ts i-th party's model. In the end, to examine the voting prediction performance of HMMs, the real voting intention of each user in the testing set was compared to the predicted voting intention, that is the party id of the party in which they were classi ed. At the end an overall score of how well the algorithm performed was calculated using the Precision, Recall and F-measure scores and then a total weighted average was estimated [ 29 ].

In Tables 2-4 we can see the results for each party of the three datasets while Table 5 shows the total weighted averages for Precision, Recall and F-measures, and the Mean Average Precision (MAP) for each dataset. The aggregate results of HMMs obtained in the Danish and Czech datasets are better than the ones obtained in the Bulgarian dataset, but without a marked di erence. The HMM classi er achieved a similar overall prediction performance for the Danish and Czech datasets, with the former to be slightly better.

In the Danish dataset the smooth distribution of samples per party (see Figure 5(a)) along with the homogeneity of answer patterns among the supporters of the same party reects in quite smooth performance across parties as it can be seen in Table 2. However, the prediction performance for the sixth party, which holds the majority of the users, exceeds the performance of the others. The third and the fth parties have the same number of users and the smallest distribution of samples in the training set. Consequently, the HMMs for these parties achieved the worst performance exhibiting high variance between recall and prediction which re ected in low F-score. Even so, the results for the third party were better than the results for the fth party. This shows that the users in the third party depict higher consistency on their answers and thus the HMM for this party was more e ective compared to that of the fth party.

The vote prediction performance of HMMs for the Czech dataset, shown in Table 3, varies signi cantly among parties. Once again the HMMs for the parties with the higher number of supporters, i.e., the tenth and fourth (see Figure 5(c)) give the best scores. The relatively low performance in vote prediction for the supporters of small parties is mainly due to insu cient number of samples. However, there are cases of parties with fewer samples, such as the third and sixth, whose HMMs performed better than parties with more samples such as the second, fth and ninth party. By carefully examining these cases in Table 3 we see that the low number of samples re ects in unbalanced recall and precision scores, which in turn lead to low F-scores. The poor performance for the other parties is possibly due to the non-homogeneity of user pro les which leads to low scores in both recall and precision. Non-homogeneity within party supporters occurs for various reasons, such as di erent political background and di erent view for the various categories of policy statements. For instance, the supporters of the same party might have a common view on economy but totally di erent in EU policy issues. As we explain later in the Conclusion section, within party clusters can be investigated separately by modeling data from each speci c cluster through a Gaussian distribution and then generating mixture of Gaussians taking into account the ratio of each source [ 4, 27 ]. It is known that whenever the distributed data are asymmetric and multi-modal, a mixture of Gaussians can be used to model them [ 10 ].

The results for the Bulgarian dataset, shown in Table 4, are more di cult to interpret. The HMM for the rst party, i.e., the one with the majority of supporters, achieved a moderate performance, while the HMM for the fourth party, which was trained on less than 100 samples, presents the second best performance. Once more, the observation made in previous datasets is con rmed: HMMs can be e ectively trained even with very small training samples when these samples form a single cluster in the U-dimensional hyperspace, where U is the number of policy statements. Nevertheless, if the number of samples is adequate but there is no or low coherence between the pro les of party-supporters then the results tend to be poor.

The overall performance of HMMs in predicting vote intention in SVAAs is quite satisfactory as it can be seen in Table 5. Thus, the use of HMMs, which make use of the conditional probabilities of the VAA user answers, seems to be working. This was expected since the policy statements in VAA questionnaires are usually correlated and grouped into categories representing speci c political issues. Therefore, answers to next policy statement can be `predicted' from previous answers. Also the policy statements are answered with a speci c display order, from the rst to last one, and is kept constant for a speci c VAA creating sequences of symbols; people who support the same party are likely to create similar sequences, since they usually share same political opinions. Thus, an HMM classi er, by utilizing answer patterns of users supporting the same party, is able to create simple and compact models that perform quite well in terms of prediction scores.

By applying HMMs to VAAs we realized that HMM classi er performance is closest to Mahalanobis classi er behavior in other VAAs, while it surpasses the performance of other machine learning algorithms, which were applied in the past to model user-party similarities (see Agathokleous et al. [ 1 ], Katakis et al. [ 15 ], Tsapatsoulis and Mendez [ 30 ], Tsapatsoulis et al. [ 29 ]). We noticed, however, that imperfect modeling happens either due to insu cient number of samples of a party or because of the inconsistency among users classi ed to the same party. Nevertheless, the nonaccurate results for small parties do not critically a ect the design of social recommendation, i.e., the overall vote intention predictions remains high, which is in agreement with the results reported by Tsapatsoulis et al. [ 29 ]. 5.

CONCLUSION

In this work we use HMM classi er in order to improve the e ectiveness of social voting recommendation feature of VAAs. We based on the idea that while the users are answering the VAA policy statements they are incrementally producing sequences of observations, i.e., answer patterns, that might characterize `typical' voters of particular parties. Thus, the ability of HMMs to capture correlations in symbol sequences would be bene cial. The performance of the proposed technique was evaluated based on the well known Recall, Precision and F-score metrics. We observed that, even if the order in which policy statements are displayed in VAAs does not actually matter, the HMMs perform very well in estimating the vote intention of users taking into account the intra-sequence correlations. This is not a surprise as the SVAAs are based on party-voters models and HMM classi er creates simple and compact models by utilizing the `path' that users of the same party create when answering the online questionnaire. Also, the policy statements in VAAs are grouped together according to the issue category that they represent. The statements that refer on the same subject are correlated and are answered similarly by the users. Therefore, answering paths are depended and next answers depend on previous answers of same category. By nding the conditional probability in which a statement is given according to category path already occurred, the HMMs can e ectively provide vote recommendation.

From our experiments we noticed that the prediction performance of HMMs depends on the consistency between the answers of the users in each party and the distribution of samples per party. Parties with the majority of users achieved the best performance in the Danish and Czech datasets. In the case of Bulgarian dataset, the HMM for the party with the highest percentage of samples presented moderate results, while the HMM for the fourth party with very few users (less than 100) achieved the second best performance. This lead us to the observation that in some cases the party-supporters pro les create a multi-modal clustering in the policy statements hyperspace (due to di erent political backgrounds and di erent views in the various categories of policy statements). In such cases the use of mixture of Gaussians [ 10 ] or di erent clustering techniques could be bene cial. In the near future we plan to tackle this problem by using per party and per category of policy statements HMMs. Thus, a combination of HMMs for party-supporters modeling will be pursued to account for the multi-modal distribution of VAA user pro les within the same party.

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