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Ideal-point models with absentions

Eduardo writes:

I’ve been thinking for a while now about how to incorporate a model of abstentions to our usual ideal point model. The idea is that there is some spatial information on the abstentions, and it might be worthwhile to use it.

In many legislatures, the level of abstention is much higher than in current American House and Senate. Jones and Hwang(forthcoming AJPS), for example, note:

There are two principal ways to deal with the reality of Chamber roll call voting. The first is to only consider votes cast as “Yes” or “No”, and code all other actions as missing. Such an approach excludes valuable information on deputy preferences and fails to account for the most prominent method of expressing dissent with the official party position.

Jones and Hwang go on and code the abstentions as Is”NO”. Is there information to be gained by incorporating a model of abstentions into an ideal point estimation model? What is needed for the resulting model to be identified?

I’ve been toying around with this idea for a while, and wrote a couple of winbugs code using a multinomial logit likelihood. However, this assumes that there is some alternative point in the policy space that legislators can express by abstaining. I would like to be more explicit in relating ideal points to abstention.

In ideal point models, one reason why one wouldn’t cast a vote is indifference.
In a one dimensional model. Conditional on voting, the utilities are (see Clinton, Jackman and Rivers, henceforth CJR):


The difference in utilities is N_j^2-Y_j^2+2(Y_j-N_j)x_i+e_{ij}-n_{ij}. CJR show that we can estimate this, assuming Var(e_{ij}-n_{ij})=\sigma_j^2, with iid errors, as Pr(yea_ij)=\Phi(\beta x_i-\alpha_j), with \beta_j=2(Y_j-N_j)/\sigma_j and \alpha_j=(Y_j^2-N_j^2)/\sigma_j.

Well, if this is the case, the the intensity of vote j for legislator i is simply abs(\beta x_i-\alpha_j) multiplied by some scalar, correct? Hence, legislator i will only vote if this utility is greater than some threshold. I propose incorporating another probit in the model:

Pr(abs_ij)=\Phi(\delta_j+\gammma abs(\beta x_i-\alpha_j))

I am not completely sure, but I think allowing a different \gamma_j for each roll call will make the model unindentified. I guess we could, however, incorporate more information on the abstention model (distance of the capital from district, for example) that has a “non-spatial” influence on abstention.

Anyway, a model along this lines runs in winbugs, but I would like to have a sense if this is something worthwhile to do (or is not so straightforward as it seems.)
Do you think this makes any sense???

My quick response:

This seems similar to an ordered logit model, which I would think would be a natural place to start.


  1. e.leoni says:

    I thought about using an ordered logit. However, I worked it out and it seems to depend on the actual positions of the "yea" and "nay" outcomes. Isn't it true that only cutpoints are identified in the ideal point model?

  2. Andrew says:

    I got a couple of comments to this by email; i'll repeat them in the next few messages.

    From Aleks:

    We have discussed abstention in our work at… I'd argue that one has

    to interpret abstention in one of the three ways: stratagem, submission or

    absence. The underlying assumption is that the representatives are

    responsible for the consequences of their actions, so we can refer to the

    true outcome of the vote in interpreting their decision. The second

    underlying assumption is to focus on the outcome as the primary focus of

    voting. This classification also appears in the working paper .

    Stratagem is a representative's intentional not-voting by letting the known

    majority make the decision. Submission is based on a representative's

    intentional not-voting because the outcome cannot be affected. Absence is

    the usual missing-at-random absent-at-random situation either due to

    possible representative's indecision or physical absence. Generally, the

    data cannot help in choosing among these three interpretations.

    I have done some quick analysis on whether abstention can be predicted from

    other roll call information, but wasn't very successful. The only robust

    finding was that some senators are missing because of physical absence. A

    more detailed analysis would be very interesting. What I'd be looking for is

    correlations between abstention/voting among representatives. If there are

    such correlations, we could infer that there was some underlying cause.

    Eduardo's proposal includes the assumption of

    not-voting-because-of-indecision/ambivalence into the ideal point voting

    model. This is certainly an improvement beyond the existing

    not-voting-at-random assumptions, but I'm not sure whether the other causes

    and interpretations of abstention are captured sufficiently well.


  3. Andrew says:

    From Eduardo:

    Aleks –

    Very interesting discussion of abstention you have both in the paper and the web site. I agree completely with you that it is very likely that abstention is not totally or even very much explained by the ideological positions. I am sure, though, that this aspect will vary greatly across the institutions.

    Case in point: I did a quick analysis using Brazilian 1989-1991 data by scaling (with the R function MCMCirt1d from Quinn and Martin's MCMCpack R functions) separately yea/nay votes, and abstain/present votes. The correlation between the posterior means is 0.23 (a regression would lead to a t-ratio around 5). I remember doing this with other periods and getting slightly higher correlations. So there seems to be some information to be extracted.

    As to the other interpretations, I have some comments: A) if submission is a factor, we would have to model abstention as increasing with the probability of being pivotal. It seems feasible to test that if we have a decent theoretical model. B) Stratagem, on the other hand, implies either that some issues are more difficult than others for some legislators, or indifference. A prediction would be that more junior legislators would abstain more often (which is probably the opposite of what happens in the US, but for an altogether different reason.) Indifference, of course, is the aspect I am trying to model.

    One last bit of comment:

    "However, one should interpret "Not Voting" as letting the majority vote for you. Since the majority is Republican, the fact that Kerry often did not vote means that he is effectively the most central of all Democrats, based on all the votes cast in 2003."

    Your argument implies that this is not quite correct: _conditional_ on other reasons for abstaining (running for president, for example) what you say might be true. In other words, it is very important to allow other reasons for abstaining into the model! To incorporate other motives for abstention, the idea is to incorporate them into a hierarchical model, so that individual characteristics would lower/increase the abstention threshold. I am trying to get a ordinal logit model to work, as suggested by Andrew.

    thanks a lot for your comments.


  4. Andrew says:

    from Aleks:

    Hi Eduardo!

    Thanks for your comments! I hope I'm not being annoying as a political

    science amateur, but your topic is quite interesting. In my brief

    examination of the field a while ago, I have not found little on abstention

    in roll call voting, although abstention in election/referendum voting is

    well-studied (and our little country ended up being a textbook case in

    Andrew et al book!).

    I've done a present/absent analysis with our method, but I've included the

    latent variables from yea/nay analysis. There it's possible to see which

    senators are both ideologically and "absent/present-ially" associated.

    Namely, if there is such a connection, we would have a greater belief in the

    absention being "meaningful." I'm attaching the resulting picture.

    The presence-absence associations are not very strong, but there are a few


    – The one centered on OUTCOME is for those who were never absent

    – the Chaffee-centered cluster… This is indeed interesting, as there has

    been a bloc-abstention! But there was only a single one.

    – the Kerry/Edwards/Lieberman/Graham cluster (expected)

    I can do this visualization for you if you have a specific data set. The US

    Senate is not very interesting here.