{"title": "How They Vote: Issue-Adjusted Models of Legislative Behavior", "book": "Advances in Neural Information Processing Systems", "page_first": 2753, "page_last": 2761, "abstract": "We develop a probabilistic model of legislative data that uses the text of the bills to uncover lawmakers' positions on specific political issues. Our model can be used to explore how a lawmaker's voting patterns deviate from what is expected and how that deviation depends on what is being voted on. We derive approximate posterior inference algorithms based on variational methods. Across 12 years of legislative data, we demonstrate both improvement in heldout predictive performance and the model's utility in interpreting an inherently multi-dimensional space.", "full_text": "How They Vote:\n\nIssue-Adjusted Models of Legislative Behavior\n\nSean M. Gerrish\u2217\n\nPrinceton University\nPrinceton, NJ 08540\n\nDavid M. Blei\n\nPrinceton University\nPrinceton, NJ 08540\n\nDepartment of Computer Science\n\nDepartment of Computer Science\n\nsgerrish@cs.princeton.edu\n\nblei@cs.princeton.edu\n\nAbstract\n\nWe develop a probabilistic model of legislative data that uses the text of the bills to\nuncover lawmakers\u2019 positions on speci\ufb01c political issues. Our model can be used\nto explore how a lawmaker\u2019s voting patterns deviate from what is expected and how\nthat deviation depends on what is being voted on. We derive approximate posterior\ninference algorithms based on variational methods. Across 12 years of legislative\ndata, we demonstrate both improvement in heldout predictive performance and the\nmodel\u2019s utility in interpreting an inherently multi-dimensional space.\n\n1\n\nIntroduction\n\nLegislative behavior centers around the votes made by lawmakers. Capturing regularity in these votes,\nand characterizing patterns of legislative behavior, is one of the main goals of quantitative political\nscience. Voting behavior exhibits enough regularity that simple statistical models, particularly ideal\npoint models, easily capture the broad political structure of legislative bodies. However, some\nlawmakers do not \ufb01t neatly into the assumptions made by these models. In this paper, we develop\na new model of legislative behavior that captures when and how lawmakers vote differently than\nexpected.\nIdeal point models assume that lawmakers and bills are represented as points in a latent space. A\nlawmaker\u2019s (stochastic) voting behavior is characterized by the relationship between her position in\nthis space and the bill\u2019s position [1, 2, 3]. Given the data of how each lawmaker votes on each bill\n(known as a roll call), we can use ideal point models to infer the latent position of each lawmaker. In\nU.S. politics, these inferred positions reveal the commonly-known political spectrum: right-wing\nlawmakers are at one extreme, and left-wing lawmakers are at the other. Figure 1 illustrates example\ninferences from an ideal point model.\nBut there are some votes that ideal point models fail to capture. For example, Ronald Paul, Republican\nrepresentative from Texas, and Dennis Kucinich, Democratic representative from Ohio, are poorly\nmodeled by ideal points because they diverge from the left-right spectrum on issues like foreign\npolicy. Because some lawmakers deviate from their party on certain issues, their positions on these\nissues are not captured by ideal point models.\nTo this end, we develop the issue-adjusted ideal point model, a latent variable model of roll-call\ndata that accounts for the contents of the bills that lawmakers are voting on. The idea is that each\nlawmaker has both a general position and a sparse set of position adjustments, one for each issue.\nThe votes on a bill depend on a lawmaker\u2019s position, adjusted for the bill\u2019s content. The text of the\nbill encodes the issues it discusses. Our model can be used as an exploratory tool for identifying\n\u2217Use footnote for providing further information about author (webpage, alternative address)\u2014not for\n\nacknowledging funding agencies.\n\n1\n\n\fFigure 1: Traditional ideal points separate Republicans (red) from Democrats (blue).\n\nexceptional voting patterns of individual legislators, and it provides a richer description of lawmakers\u2019\nvoting behavior than the models traditionally used in political science.\nIn the following sections, we develop our model and describe an approximate posterior inference\nalgorithm based on variational methods. We analyze six Congresses (12 years) of legislative data\nfrom the United States Congress. We show that our model gives a better \ufb01t to legislative data and\nprovides an interesting exploratory tool for analyzing legislative behavior.\n\n2 Exceptional issue voting\n\nWe \ufb01rst review ideal point models of legislative roll call data and discuss their limitations. We then\npresent a model that accounts for how legislators vote on speci\ufb01c issues.\nModeling politics with ideal points.\nIdeal point models are based on item response theory, a statistical theory that models how members\nof a population judge a set of items. Applied to voting records, one-dimensional ideal point models\nplace lawmakers on an interpretable political spectrum. These models are widely used in quantitative\npolitical science [3, 4, 5].\nOne-dimensional ideal point models posit an ideal point xu \u2208 R for each lawmaker u. Each bill d is\ncharacterized by its polarity ad and its popularity bd.1 The probability that lawmaker u votes \u201cYes\u201d\non bill d is given by the logistic regression\n\np(vud = yes| xu, ad, bd) = \u03c3(xuad + bd),\n\n(1)\n\n1+exp(s) is the logistic function.2 When the popularity of a bill bd is high, nearly\nwhere \u03c3(s) = exp(s)\neveryone votes \u201cYes\u201d; when the popularity is low, nearly everyone votes \u201cNo\u201d. When the popularity\nis near zero, the probability that a lawmaker votes \u201cYes\u201d depends on how her ideal point xu interacts\nwith bill polarity ad. The variables ad, bd, and xu are usually assigned standard normal priors [3].\nGiven a matrix of votes, we can infer the ideal point of each lawmaker. We illustrate ideal points \ufb01t\nto votes in the U.S. House of Representatives from 2009-2010 in Figure 1. The model has clearly\nseparated lawmakers by their political party (colour) and provides an intuitive measure of their\npolitical leanings.\nLimitations of ideal point models. A one-dimensional ideal point model \ufb01t to the U.S. House from\n2009-2010 correctly models 98% of lawmakers\u2019 votes on training data. But it only captures 83% of\nBaron Hill\u2019s (D-IN) votes and 80% of Ronald Paul\u2019s (R-TX) votes. Why is this?\nThe ideal point model assumes that lawmakers are ordered. Each bill d splits them at a cut point\n\u2212 bd\n. Lawmakers to one side of the cut point are more likely to support the bill, and lawmakers to\nthe other side are likely to reject it. For lawmakers like Paul and Hill, this assumption is too strong\nbecause their voting behavior does not \ufb01t neatly into a single ordering. Their location among the\nother lawmakers changes with different bills.\nLawmakers do not vote randomly, however. They vote consistently within individual areas of policy,\nsuch as foreign policy and education. For example, Rep. Paul consistently votes against United States\ninvolvement in foreign military engagements, a position that contrasts with other Republicans.\nWe refer to voting behavior like this as issue voting. An issue is any federal policy area, such as\n\u201c\ufb01nancial regulation,\u201d \u201cforeign policy,\u201d \u201ccivil liberties,\u201d or \u201ceducation,\u201d on which lawmakers are\nexpected to take positions. Lawmakers\u2019 positions on these issues often diverge from their traditional\nleft/right stances. The model we will develop captures these deviations. Some examples are illustrated\n\nad\n\n1These are sometimes called the discrimination and dif\ufb01culty, respectively.\n2Many ideal point models use a probit function instead [1, 3].\n\n2\n\n\u22122\u221210123\fFigure 2: In a traditional ideal point model, lawmakers\u2019 ideal points are static (top line of each \ufb01gure).\nIn the issue-adjusted ideal point model, lawmakers\u2019 ideal points change when they vote on certain\nissues, such as Taxation.\n\nTerrorism\nterrorist\nseptember\n\nattack\nnation\nyork\n\nterrorist attack\n\nhezbolah\n\nnational guard\n\nCommemorations Transportation\ntransportation\n\nnation\npeople\n\nlife\nworld\nserve\npercent\n\nminor\nprint\ntax\nland\nguard\n\ncommunity\n\nfamily\n\ncoast guard\nsubstitute\n\nLabeled topics\n\nThe issue-adjusted ideal point model\nFigure 3: Left: Top words from topics \ufb01t using labeled LDA [6]. Right: the issue-adjusted ideal point\nmodel, which models votes vud from lawmakers and legislative items. Classic item response theory\nmodels votes v using xu and ad, bd. For our work, documents\u2019 issue vectors \u03b8 were estimated \ufb01t with\na topic model (left of dashed line) using bills\u2019 words w and labeled topics \u03b2. Expected issue vectors\nEq [\u03b8|w] are then treated as constants in the issue model (right of dashed line).\n\nin Figure 2; Charles Djou is more similar to Republicans on Taxation (right) and more similar to\nDemocrats on Health (left), while Ronald Paul is more Republican-leaning on Health and less\nextreme on Taxation. The model we will introduce uses lawmakers\u2019 votes and the text of bills to\nmodel deviations like this, on a variety of issues. This allows us to take into account whether a bill\nwas about Taxation or Education (or both) when predicting a lawmaker\u2019s vote.\nIssue-adjusted ideal points.\nWe now describe the issue-adjusted ideal point model, a new model of lawmaker behavior that takes\ninto account both the content of the bills and the voting patterns of the lawmakers. We build on the\nideal point model so that each lawmaker\u2019s ideal point can be adjusted for each issue.\nSuppose that there are K issues in the political landscape. We will use the words wd of each bill d to\ncode it with a mixture \u03b8d of issues, where each element \u03b8dk corresponds to an issue; the components\nof \u03b8d are positive and sum to one. (These vectors will come from a topic model, which we describe\nbelow.) In our proposed model, each lawmaker is also associated with a K-vector zu \u2208 RK, which\ndescribes how her ideal point changes for bills about each issue.\nWe use these variables in a model based on the traditional ideal point model of Equation 1. As above,\nxu is the ideal point for lawmaker u and ad, bd are the polarity and popularity of bill d. In our model,\nvotes are modeled with a logistic regression\n\n(2)\nwhere we use an estimate Eq [\u03b8d|wd] of the bill\u2019s issue vector from its words wd as described below.\nWe put standard normal priors on the ideal points, polarity, and dif\ufb01culty variables. We use Laplace\npriors for zu: p(zuk | \u03bb1) \u221d exp (\u2212\u03bb1||zuk||1). This enforces a sparse penalty with MAP inference\nand a \u201cnearly-sparse\u201d penalty with Bayesian inference. See Figure 3 (left) for the graphical model.\n\nu\n\nEq [\u03b8d|wd] + xu)ad + bd\n\np(vud|ad, bd, zu, xu, wd) = \u03c3(cid:0)(z(cid:62)\n\n(cid:1) ,\n\n3\n\nTaxation-adjusted ideal pointIdeal pointRobert BerryEric CantorJesse JacksonTimothy JohnsonDennis KucinichJames MarshallRonald PaulMichael McCaulHarry MitchellAnh Cao\u22122024Ideal pointXA ,BV\u03b8ZuudddudNNUDWNWZ\u03b1\u03b2K\fTo better understand the model, assume that bill d is only about Finance. This means that \u03b8d has a\none in the Finance dimension and zero everywhere else. With a classic ideal point model, a lawmaker\nu\u2019s ideal point, xu, gives his position on each issue, including Finance. With the issue-adjusted ideal\npoint model, his effective ideal point for Finance, xu + zu,Finance, gives his position on Finance. The\nadjustment zu,Finance affects how lawmaker u feels about Finance alone. When zu,k = 0 for all u, k,\nthe model becomes the classic ideal point model.\nThis model lets us inspect lawmakers\u2019 overall voting patterns by issue. Given a collection of votes\nand a coding of bills to issues, posterior estimates of the ideal points and per-issue adjustments give\nus a window into voting behavior that is not available to classic ideal point models.\nUsing Labeled LDA to associate bills with issues.\nEquation 2 adjusts a lawmaker\u2019s ideal point by using the conditional expectation of a bill\u2019s thematic\nlabels \u03b8d given its words wd. We estimate this vector using labeled latent Dirichlet allocation\n(LDA) [6]. Labeled LDA is a topic model, a bag-of-words model that assumes a set of themes for the\ncollection of bills and that each bill exhibits a mixture of those themes. The themes, called topics, are\ndistributions over a \ufb01xed vocabulary. In unsupervised LDA [7] they are learned from the data. In\nlabeled LDA, they are de\ufb01ned by using an existing tagging scheme. Each tag is associated with a\ntopic; its distribution is found by taking the empirical distribution of words for documents assigned\nto that tag.3 This gives interpretable names (the tags) to the topics.\nWe used tags provided by the Congressional Research Service [8], which provides subject codes\nfor all bills passing through Congress. These subject codes describe the bills using phrases which\ncorrespond to traditional issues, such as Civil rights and National security. Each bill may cover\nmultiple issues, so multiple codes may apply to each bill. (Many bills have more than twenty labels.)\nWe used the 74 most-frequent issue labels. Figure 3 (right) illustrates the top words from several\nof these labeled topics.4 We \ufb01t the issue vectors E [\u03b8d|wd] as a preprocessing step. In the issue-\nadjusted ideal point model (Equation 2), E [\u03b8d] was treated as observed when estimating the posterior\ndistribution p(xu, ad, bd, zd|E [\u03b8d|wd] , vud). We summarize all 74 issue labels in \u00a7A.2.5\nRelated Work. Item response theory has been used for decades in political science [3, 4, 5]; see\nEnelow and Hinich for a historical perspective [9] and Albert for Bayesian treatments of the model\n[10]. Some political scientists have used higher-dimensional ideal points, where each legislator is\nattached to a vector of ideal points xu \u2208 RK and each bill polarization ad takes the same dimension\nu ad + bd). The principal component of\nK [11]. The probability of a lawmaker voting \u201cYes\u201d is \u03c3(xT\nideal points explains most of the variance and explains party af\ufb01liation. However, other dimensions\nare not attached to issues, and interpreting beyond the principal component is painstaking [2].\nRecent work in machine learning has provided joint models of legislative text and the bill-making\nprocess. This includes using transcripts of U.S. Congressional \ufb02oor debates to predict whether\nspeeches support or oppose pending legislation [12] and predicting whether a bill will survive\ncongressional committee by incorporating a number of features, including bill text [13]. Other work\nhas aimed to predict individual votes. Gerrish and Blei aimed to predict votes on bills which had not\nyet received any votes [14]. Their model \ufb01ts ad and bd using supervised topics, but the underlying\nvoting model was one-dimensional: it could not model individual votes better than a one-dimensional\nideal point model. Wang et al. created a Bayesian nonparametric model of votes and text over time\n[15]. We note that these models have different purposes from ours, and neither addresses individuals\u2019\naf\ufb01nity toward issues.\nThe issue-adjusted model is conceptually more similar to recent models for content recommendation.\nWang and Blei describe a method to recommend academic articles to individuals [16], and Agarwal\nand Chen propose a model to match users to Web content [17]. Though they do not consider roll-call\ndata, these recommendation models also try to match user behavior with textual item content.\n\n3Ramage et al. explore more sophisticated approaches [6], but we found this simpli\ufb01ed version to work well.\n4After de\ufb01ning topics, we performed two iterations of LDA with variational inference to smooth the topics.\n5We refer to speci\ufb01c sections in the supplementary materials (appendix) as \u00a7A.#.\n\n4\n\n\f3 Posterior estimation\n\nThe central computational challenge in this model is to uncover lawmakers\u2019 issue preferences zu\nby using the their votes v and bills\u2019 issues \u03b8d. We do this by estimating the posterior distribution\np(x, z, a, b|v, \u03b8). Bayesian ideal point models are usually \ufb01t with Gibbs sampling [2, 3, 5, 18].\nHowever, fast Gibbs samplers are unavailable for our model because the conditionals needed are not\nanalytically computable. We estimate the posterior with variational Bayes.\nIn variational Bayes, we posit a family of distributions {q\u03b7} over the latent variables that is likely\nto contain a distribution similar to the true posterior [19]. This variational family is indexed by\nparameters \u03b7, which are \ufb01t to minimize the KL divergence between the variational and true posteriors.\nSpeci\ufb01cally, we let {q\u03b7} be the family of fully factorized distributions\n\nq(x, z, a, b|\u03b7) =(cid:89)\n\n)N (zu|\u02dczu, \u03bbzu)(cid:89)\n\nD\n\nN (xu|\u02dcxu, \u03c32\n\nxu\n\nU\n\nN (ad|\u02dcad, \u03c32\n\nad\n\n)N (bd|\u02dcbd, \u03c32\n\nbd\n\n),\n\n(3)\n\nwhere we parameterize the variational posterior with \u03b7 = {(\u02dcxu, \u03c3x), (\u02dczu, \u03c3zu), (\u02dca, \u03c3a), (\u02dcb, \u03c3b)}. We\nassumed full factorization to make inference tractable. Though simpler than the true posterior, \ufb01tted\nvariational distributions can be excellent proxies for it. The similarity between ideal points \ufb01t with\nvariational inference and MCMC has been demonstrated in Gerrish in Blei [14].\nVariational inference usually proceeds by optimizing the variational objective\nL\u03b7 = Eq\u03b7 [log p(x, z, a, b, v, \u03b8)] \u2212 Eq\u03b7 [log q\u03b7(x, z, a, b)]\n\n(4)\nwith gradient or coordinate ascent (this is equivalent to optimizing the KL divergence between q and\nthe posterior). Optimizing this bound is challenging when the expectation is not analytical, which\nmakes computing the exact gradient \u2207\u03b7L\u03b7 more dif\ufb01cult. We optimize this bound with stochastic\ngradient ascent [20, 21], approximating the gradient with samples from q\u03b7;\n\n\u2207\u03b7L\u03b7 \u2248 1\nM\n\n(log p(ym, v, \u03b8) \u2212 log q\u03b7(ym));\n\n\u2202q\u03b7\n\u2202\u03b7\n\n(5)\n\n(cid:88)\n\nym\u223cq\u03b7\n\nwhere ym = (xm, zm, am, bm) is a sample from q\u03b7. The algorithm proceeds by following this\nstochastic gradient with decreasing step size; we provide further details in \u00a7A.1.\n\n4 Analyzing twelve years of U.S. legislative history\n\nWe used our model to investigate twelve years of U.S. legislative history. We compare the posterior \ufb01t\nwith this model to the same data \ufb01t with traditional ideal points and validate the model quantitatively.\nWe then provide a closer look at the collection of issues, lawmakers, and bills and explore several\ninteresting results of the model.\n\n4.1 Data and Experiment Setup\n\nWe studied U.S. Senate and House of Representative roll-call votes from 1999 to 2010. This period\nspanned Congresses 106 to 111 and covered an historic period in recent U.S. politics, the majority\nof which Republican President George W. Bush held of\ufb01ce. Bush\u2019s inauguration and the attacks\nof September 11th, 2001 marked the \ufb01rst quarter of this period, followed by the wars in Iraq and\nAfghanistan. Congress became more partisan over this period, and Democratic President Obama was\ninaugurated in January 2009.\nWe provide a more complete summary of statistics for our datasets in \u00a7A.3. For context, the median\nsession we considered had 540 lawmakers, 507 bills, and 201,061 votes in both the House and Senate.\nAltogether, there were 865 unique lawmakers, 3,113 bills, and 1,208,709 votes.\nCorpus preparation. For each congress, we considered only bills for which votes were explicitly\nrecorded in a roll-call. We ignored votes on bills for which text was unavailable. To \ufb01t the labeled\ntopic model to each bill, we removed stop words and grouped common phrases as n-grams. All bills\nwere downloaded from www.govtrack.us [22], a nonpartisan website which provides records\nof U.S. Congressional voting. We \ufb01t the Senate and House separately for each two-year Congress\nbecause lawmakers\u2019 strategies change at each session boundary.\n\n5\n\n\fTable 1: Average log-likelihood of heldout votes using six-fold cross validation. These results cover\nCongresses 106 to 111 (1999-2010) with regularization \u03bb = 1. The issue-adjusted model yields\nhigher heldout log-likelihood for all congresses in both chambers than a standard ideal point model.\nPerm. Issue illustrates the issue model \ufb01t when bills\u2019 issue labels were randomly permuted. Perm.\nIssue is results for the issue model \ufb01t using permuted document labels.\n\nModel\nCongress\n\n107\n\n106\n111\n-0.209 -0.209 -0.182 -0.189 -0.206 -0.182\n-0.208 -0.209 -0.181 -0.188 -0.205 -0.180\nPerm. Issue -0.210 -0.210 -0.183 -0.203 -0.211 -0.186\n\nIdeal\nIssue\n\n108\n\nSenate\n\n109\n\n110\n\nIdeal\nIssue\n\n-0.168 -0.154 -0.096 -0.120 -0.090 -0.182\n-0.166 -0.147 -0.093 -0.116 -0.087 -0.180\nPerm. Issue -0.210 -0.211 -0.100 -0.123 -0.098 -0.187\n\nHouse\n\n4.2 Comparison of classic and exploratory ideal points\n\nHow do classic ideal points compare with issue-adjusted ideal points? We \ufb01t classic ideal points\nto the 111th House (2009 to 2010) to compare them with issue-adjusted ideal points \u02dcxu from the\nsame period, using regularization \u03bb = 1. The models\u2019 ideal points \u02dcxu were very similar, correlated\nat 0.998. While traditional ideal points cleanly separate Democrats and Republicans in this period,\nissue-adjusted ideal points provide an even cleaner break between the parties. Although the issue-\nadjusted model is able to use other parameters\u2014lawmakers\u2019 adjustments \u02dczu\u2014to separate the parties\nbetter, the improvement is much greater than expected by chance (p < 0.001 using a permutation\ntest).\n\n4.3 Evaluation and signi\ufb01cance\n\nWe \ufb01rst evaluate the issue-adjusted model by measuring how it can predict held out votes. (This is a\nmeasure of model \ufb01tness.) We used six fold cross-validation. For each fold, we computed the average\npredictive log-likelihood log p(vudTest|vudTrain) = log p(vudTest|\u02dcxu, \u02dczu, \u02dcad, \u02dcbd, Eq [\u03b8d|w]) of the test\nvotes and averaged this across folds. We compared these with the ideal point model, evaluating the\nlatter in the same way. We give implementation details of the model \ufb01t in \u00a7A.1.\nNote that we cannot evaluate how well this model predicts votes on a heldout bill d. As with the ideal\npoint model, our model cannot predict \u02dcad, \u02dcbd without votes on d. Gerrish and Blei [14] accomplished\nthis by predicting \u02dcad and \u02dcbd using the document\u2019s text. (Combining these two models would be\nstraightforward.)\nPerformance. We compared the issue-adjusted model\u2019s ability to represent heldout votes with the\nideal point model. We \ufb01t the issue-adjusted model to both the House and Senate for Congresses 106\nto 110 (1999-2010) with regularization \u03bb = 1. For comparison we also \ufb01t an ideal point model to\neach of these congresses. In all Congresses and both chambers, the issue-adjusted model represents\nheldout votes with higher log-likelihood than an ideal point model. We show these results in Table 1.\nSensitivity to regularization. To measure sensitivity to parameters, we \ufb01t the issue-adjusted model\nto the 109th Congress (1999-2000) of the House and Senate for a range \u03bb = 0.0001, . . . , 1000 of\nB = exp(\u22125). The variational implementation\nregularizations. We \ufb01xed variance \u03c32\ngeneralized well for the entire range, with heldout log likelihood highest for 1 \u2264 \u03bb \u2264 10.\nPermutation test. We used a permutation test to understand how the issue-adjusted model improves\nupon ideal point models. This test strengthens the argument that issues (and not some other model\nchange, such as the increase in dimension) help to improve predictive performance. To do this test,\nwe randomly permuted topic vectors\u2019 document labels to completely remove the relationship between\ntopics and bills: (\u03b81, . . . , \u03b8D) (cid:55)\u2192 (\u03b8\u03c0i(1) . . . \u03b8\u03c0i(D)), for \ufb01ve permutations \u03c01, . . . , \u03c05. We then \ufb01t\nthe issue model using these permuted document labels. As shown in Table 1, models \ufb01t with the\noriginal, unpermuted issues always formed better predictions than models \ufb01t with the permuted issues.\nFrom this, we draw the conclusion that issues indeed help the model to represent votes.\n\nX , \u03c32\n\nA, \u03c32\n\nZ, \u03c32\n\n6\n\n\fFigure 4: Ideal points xu and issue-adjusted ideal points xu + zuk from the 111th House for the\nFinance issue. Republicans (red) saw more adjustment than Democrats (blue).\n\nRon Paul Offsets \u02c6zu,k\n\nDonald Young Offsets \u02c6zu,k\n\nFigure 5: Signi\ufb01cant issue adjustments for exceptional senators in Congress 111. Statistically\nsigni\ufb01cant issue adjustments are shown with each \u00d7.\n\n4.4 Analyzing issues, lawmakers, and bills\n\nIn this section we take a closer look at how issue adjustments improve on ideal points and demonstrate\nhow the issue-adjusted ideal point model can be used to analyze speci\ufb01c lawmakers. We focus on an\nissue-adjusted model \ufb01t to all votes in the 111th House of Representatives (2009-2010).\nWe can measure the improvement by comparing the training likelihoods of votes in the issue-adjusted\nand traditional ideal point models. The training log-likelihood of each vote is\n\nwhere p = (\u02dcxu + \u02dczT\nu\nmodel. The corresponding log-likelihood Iud under the ideal point model is p = \u02dcxu\u02dcad + \u02dcbd.\n\n(6)\nEq [\u03b8d|w])\u02dcad + \u02dcbd is the log-odds of a vote under the issue adjusted voting\n\nJud = 1{vud=Yes }p \u2212 log(1 + exp(p)),\n\n4.4.1 Per-issue improvement\n\nTo inspect the improvement of issue k, for example, we take the sum of the improvement in log-\nlikelihood weighted by each issue:\n\n(cid:80)\n\n(cid:80)\nEq [\u03b8dvk|w] (Jud \u2212 Iud)\n\nEq [\u03b8dvk|w]\n\nVud\n\nImpk =\n\nVud\n\n.\n\n(7)\n\nA high value of Impk indicates that issue k is associated with an increase in log-likelihood, while a\nlow value indicates that the issue saw a decrease in log-likelihood.\nProcedural issues such as Congressional sessions (in contrast to substantive issues) were among the\nmost-improved issues; they were also much more partisan. This is a result predicted by procedural\ncartel theory [23, 24, 25, 26], which posits that lawmakers will be more polarized in procedural\nvotes (which describe how Congress will be run) than substantive votes (the issues discussed during\nelections). A substantive issue which was better-predicted was Finance, which we illustrate in\nFigure 4. Infrequent issues like Women and Religion were nearly unaffected by lawmakers\u2019 offsets.\nIn \u00a7A.4, we illustrate Impk for all issues.\n\n7\n\n\u22122024Ideal pointRonald PaulRobert BerryEric CantorJesse JacksonTimothy JohnsonDennis KucinichJames MarshallMichael McCaulHarry MitchellAnh CaoIdeal pointFinance-adjusted ideal point\u22123\u2212113Congressional sessionsPublic lands and natural resourcesHouse rules and procedureRacial and ethnic relationsLawSpecial monthsHealthCrime and law enforcementInternational affairsHuman rights\u22123\u2212113Land transfersHealthRacial and ethnic relationsChildrenFinanceAppropriationsNatural resourcesSocial workAnniversariesGovernment information and archivesCrime and law enforcementCommemorative events and holidays\f4.4.2 Per-lawmaker improvement\n\nIn the 111th House, the per-lawmaker improvement Impu =(cid:80)\n\nD(Jud \u2212 Iud) was invariably positive\nor negligible, because each lawmaker has many more parameters in the issue-adjusted model. Some\nof most-improved lawmakers were Ron Paul and Donald Young.\nWe corrected lawmakers\u2019 issue adjustments to account for their left/right leaning and performed\npermutation tests as in \u00a74.3 to \ufb01nd which of these corrected adjustments \u02c6zuk were statistically\nsigni\ufb01cant at p < 0.05 (see supplementary section \u00a7A.5 for how we obtain \u02c6zuk from zuk and \u00a7A.5 for\ndetails on the permutation test). We illustrate these issue adjustments for Paul and Young in Figure 5.\nRon Paul. Paul\u2019s offsets were extreme; he voted more conservatively than expected on Health,\nHuman rights and International affairs. He voted more liberally on social issues such as Racial and\nethnic relations. The issue-adjusted training accuracy of Paul\u2019s votes increased from 83.8% to 87.9%\nwith issue offsets, placing him among the two most-improved lawmakers with this model.\nThe issue-adjusted improvement ImpK (Equation 7), when restricted to Paul\u2019s votes, indicate signi\ufb01-\ncant improvement in International affairs and East Asia (he tends to vote against U.S. involvement\nin foreign countries); Congressional sessions; Human rights; and Special months (he tends to vote\nagainst recognition of special months and holidays). The model hurt performance related to Law,\nRacial and ethnic relations, and Business, none of which were statistically signi\ufb01cant issues for Paul.\nDonald Young. One of the most exceptional legislators in the 111th House was Alaska Republican\nDonald Young. Young stood out in a topic used frequently in House bills about naming local\nlandmarks. Young voted against the majority of his party (and the House in general) on a series of\nlargely symbolic bills and resolutions. In an Agriculture topic, Young voted (with only two other\nRepublicans and against the majority of the House) not to commend \u201cmembers of the Agri-business\nDevelopment Teams of the National Guard [to] increase food production in war-torn countries.\u201d\nYoung\u2019s divergent voting was also evident in a series of votes against naming various landmarks\u2013such\nas post of\ufb01ces\u2013in a topic about such symbolic votes. Notice that Young\u2019s ideal point is not particularly\ndistinctive: using the ideal point alone, we would not recognize his unique voting behavior.\n\n4.4.3 Per-bill improvement\n\nPer-bill improvement Impd =(cid:80)\n\nU (Jud \u2212 Iud) decreased for some bills. The bill which decreased\nthe most from the ideal point model in the 111th House was the Consolidated Land, Energy, and\nAquatic Resources Act of 2010 (H.R. 3534). This bill had substantial weight in \ufb01ve issues, with most\nin Public lands and natural resources, Energy, and Land transfers, but its placement in many issues\nharmed our predictions. This effect\u2014worse performance on bills about many issues\u2014suggests that\nmethods which represent bills more sparsely may perform better than the current model.\n\n5 Discussion\n\nTraditional models of roll call data cannot capture how individual lawmakers deviate from their latent\nposition on the political spectrum. In this paper, we developed a model that captures how lawmakers\nvary, issue by issue, and used the text of the bills to attach speci\ufb01c votes to speci\ufb01c issues. We\ndemonstrated, across 12 years of legislative data, that this model better captures lawmaker behavior.\nWe also illustrated how to use the model as an exploratory tool of legislative data.\nFuture areas of work include incorporating external behavior by lawmakers. For example, lawmakers\nmake some (but not all) issue positions public. Many raise campaign funds from interest groups.\nMatching these data to votes would help us to understand what drives lawmakers\u2019 positions.\n\nAcknowledgments\n\nWe thank the reviewers for their helpful comments. David M. Blei is supported by ONR N00014-11-\n1-0651, NSF CAREER 0745520, AFOSR FA9550-09-1-0668, the Alfred P. Sloan foundation, and a\ngrant from Google.\n\n8\n\n\fReferences\n[1] Keith T. Poole and Howard Rosenthal. Patterns of congressional voting. American Journal of Political\n\nScience, 35(1):228\u2013278, February 1991.\n\n[2] Simon Jackman. Multidimensional analysis of roll call data via Bayesian simulation: Identi\ufb01cation,\n\nestimation, inference, and model checking. Political Analysis, 9(3):227\u2013241, 2001.\n\n[3] Joshua Clinton, Simon Jackman, and Douglas Rivers. The statistical analysis of roll call data,. American\n\nPolitical Science Review, 98(2):355\u2013370, 2004.\n\n[4] Keith T. Poole and Howard Rosenthal. A spatial model for legislative roll call analysis. American Journal\n\nof Political Science, pages 357\u2013384, 1985.\n\n[5] Andrew D. Martin and Kevin M. Quinn. Dynamic ideal point estimation via Markov chain Monte Carlo\n\nfor the U.S. Supreme Court, 1953-1999. Political Analysis, 10:134\u2013153, 2002.\n\n[6] Daniel Ramage, David Hall, Ramesh Nallapati, and Christopher D. Manning. Labeled LDA: A supervised\ntopic model for credit attribution in multi-labeled corpora. Proceedings of the 2009 Conference on\nEmpirical Methods in Natural Language Processing, 2009.\n\n[7] David M. Blei, Andrew Y. Ng, and Michael I. Jordan. Latent Dirichlet allocation. Journal of Machine\n\nLearning Research, pages 993\u20131022, 2003.\n\n[8] Congressional research service. Available http://www.loc.gov/crsinfo/, 2011.\n[9] James M. Enelow and Melvin J. Hinich. The Spatial Theory of Voting: An Introduction. Cambridge\n\nUniversity Press, New York, 1984.\n\n[10] James Albert. Bayesian estimation of normal ogive item response curves using Gibbs sampling. Journal of\n\nEducational Statistics, 17:251\u2013269, 1992.\n\n[11] James J. Heckman and James M. Snyder. Linear probability models of the demand for attributes with an\nempirical application to estimating the preferences of legislators. RAND Journal of Economics, 27(0):142\u2013\n189, 1996.\n\n[12] Matt Thomas, Bo Pang, and Lillian Lee. Get out the vote: Determining support or opposition from\ncongressional \ufb02oor-debate transcripts. In Proceedings of the 2006 Conference on Empirical Methods on\nNatural Language Processing, 2006.\n\n[13] Tae Yano, Noah A. Smith, and John D. Wilkerson. Textual predictors of bill survival in congressional\ncommittees. In Proceedings of the 2012 Conference of the North American Chapter of the Association for\nComputational Linguistics, page 793802, 2012.\n\n[14] Sean Gerrish and David Blei. Predicting legislative roll calls from text. Proceedings of the International\n\nConference on Machine Learning, 2011.\n\n[15] Eric Wang, Dehong Liu, Jorge Silva, David Dunson, and Lawrence Carin. Joint analysis of time-evolving\nbinary matrices and associated documents. Advances in Neural Information Processing Systems, 23:2370\u2013\n2378, 2010.\n\n[16] Chong Wang and David M. Blei. Collaborative topic modeling for recommending scienti\ufb01c articles.\nIn Proceedings of the 17th international conference on Knowledge Discovery and Data mining, pages\n448\u2013456, 2011.\n\n[17] Deepak Agarwal and Bee-Chung Chen. fLDA: Matrix factorization through latent Dirichlet allocation.\nProceedings of the Third ACM International Conference on Web Search and Data Mining, pages 91\u2013100,\n2010.\n\n[18] Valen E. Johnson and James H. Albert. Ordinal Data Modeling. Springer-Verlag, New York, 1999.\n[19] Michael I. Jordan, Zoubin Ghahramani, Tommi S. Jaakkola, and Lawrence K. Saul. An introduction to\n\nvariational methods for graphical models. Learning in Graphical Models, pages 183\u2013233, 1999.\n\n[20] Herbert Robbins and Sutton Monro. A stochastic approximation method. Annals of Mathematical Statistics,\n\n22(3), September 1951.\n\n[21] Leon Bottou and Yann Le Cun. Large scale online learning. In Advances in Neural Information Processing\n\nSystems, 2004.\n\n[22] Govtrack.us, 2010. Civic Impulse LLC. Available http://www.govtrack.us.\n[23] Richard F. Fenno Jr. The Congress and America\u2019s Future. Prentice-Hall, Englewood Cliffs, NJ, 1965.\n[24] Gary W. Cox and Mathew D. McCubbins. Legislative Leviathon. University of California Press., 1993.\n[25] Gary W. Cox and Keith T. Poole. On measuring partisanship in roll-call voting: The U.S. House of\n\nRepresentatives, 1877-1999. American Journal of Political Science, 46(3):pp. 477\u2013489, 2002.\n\n[26] Gary W. Cox and Mathew D. McCubbins. Setting the Agenda: Responsible Party Government in the U.S.\n\nHouse of Representatives. Cambridge University Press, 2005.\n\n9\n\n\f", "award": [], "sourceid": 1268, "authors": [{"given_name": "Sean", "family_name": "Gerrish", "institution": null}, {"given_name": "David", "family_name": "Blei", "institution": null}]}