Finding the factions in Congress from votes alone

Every recorded vote in the House is public. How much can you learn about who stands where, and which methods can you trust?

The standard data-science tutorial on this goes: download Congress’s roll-call votes, run PCA or k-means, and watch the Democrats and Republicans fall into two neat clouds. It looks impressive, and it proves almost nothing. Any method separates the two parties. The interesting questions are inside each party: who sits where, how sure can we be, and are there real factions or just a smooth spread?

I compared three ways of placing members on a map and five ways of finding groups, and checked each one against answers the votes never saw. Code, results and executed notebooks: github.com/godot107/ideology-clusters.

The trap: “it separates the parties” proves little

Lay the votes out as a table, one row per member, one column per vote, yes or no in each cell. Plain PCA on the 118th House (2023-24) matches DW-NOMINATE, political science’s standard scores, at a correlation of 0.97. That sounds like a near-perfect result.

Now score it within each party, the way you’d need it to work if you wanted to know which Democrats are more progressive or which Republicans are more hard-line. The agreement drops to 0.52 among Democrats and 0.82 among Republicans. Almost all of that 0.97 came from the two parties being far apart. So every method in this project is scored within party, and splitting the parties counts for nothing.

Grading against a Congress I built

The catch with real votes is that nobody knows members’ “true” positions. DW-NOMINATE is a useful comparison, but it’s a model too: it pools each member’s whole career. So I also built a synthetic Congress: 440 members in six factions, with positions I chose, noisy votes and realistic absences (chronic absentees, members who joined late). There, every method can be graded exactly.

The difference is how they handle missed votes. PCA treats yes/no as numbers and fills each missing vote with an average, which drags absentees toward the middle. Logistic PCA models the chance of a yes and simply skips votes that weren’t cast.

How many dimensions does Congress have?

On real votes there’s no answer key, so I hid a random 10% of the 118th House’s votes and predicted them. The rival to beat is trivial: “every member votes with their party’s majority”.

The party rule alone gets 93%. One left-right scale adds less than 3 points, and extra dimensions add less than one more. That matches decades of political science: modern Congress is close to one-dimensional.

Error bars, and when they lie

A position without an error bar hides how much the data actually supports it. So I fitted the standard Bayesian ideal-point model (Clinton, Jackman & Rivers, 2004) in NumPyro, which gives every member a range.

The wide ranges make sense once you look at who has them: members sworn in late after a special election, members who left early, and members at the far edge of their party, where no vote separates them from their neighbours. Within party, this model agrees best with DW-NOMINATE: 0.90 among Republicans and 0.72 among Democrats (0.89 and 0.75 in the current House).

But the synthetic Congress caught something. For five of the six factions, the 90% ranges contained the true position 77-91% of the time, close to the promised 90%. For the sixth, a faction I’d made different on a second dimension (voting against its own leadership), they contained it only 25% of the time. A one-dimensional model has nowhere to put that difference, so it squeezes those members onto the left-right line and reports narrow ranges around the wrong spot. Error bars are only as honest as the model behind them.

The fix is to give the model somewhere to put it. With a second dimension, the same faction’s ranges contain the truth 93% of the time on left-right (95% on the second dimension), and the other five stay at 82-97%. Getting there took one more lesson: these models only loosely fix where the axes point, so the sampler’s runs slowly drift and rotate, and the raw diagnostics looked like total failure. Lining every draw up on a common map (a rotation that moves nobody relative to anybody else) showed the runs had agreed all along.

Factions: five methods, one trade-off

Next, clustering. I compared k-means with a Gaussian mixture (soft membership: “70% this group”), HDBSCAN (dense regions, with members in between as noise), Ward hierarchical clustering, and community detection on a co-voting network. Each picked its own number of groups by its standard rule.

On the synthetic Congress, the honest finding was this: k-means, the mixture and Ward all found three groups (Democrats, Republicans and the faction that differs in kind). The factions that differed only by degree (a wing, a mainstream, moderates) formed a continuum with no gap between them, so there was nothing to find. Telling k-means the “right” answer of six groups made it score worse, because it then cuts the continuum at arbitrary points.

On the current 119th House, I checked each method against caucus membership, which the votes never saw. F1 measures how well one cluster captures a caucus within its party (1 = exactly). Stability is how similar the clustering stays when the roll calls are resampled (1 = identical).

Explore the map yourself: hover over any member, highlight a caucus, or search by name.

The methods that find the most faction structure are the least stable. HDBSCAN is rock-steady because it mostly just returns the two parties. Network communities isolate most of the Progressive Caucus but reshuffle the most between resamples. There’s no single best method. The useful habit is to report clusters together with their stability, and to use soft membership for the 86 members who don’t belong more than 80% to any one group.

So what is the second dimension?

In the map, Freedom Caucus members sit at the bottom of the Republican cloud. The axis has no label of its own, so I went back to the votes. For every roll call where at least 5% of a party broke with its majority, I asked which dimension predicts who broke away.

Among Republicans, left-right barely does (correlation 0.07). Dimension 2 does (0.36), and most clearly on “suspension” bills, the fast-tracked, two-thirds-majority bills that are in practice the bipartisan ones (0.61). One reading fits both parties: dimension 2 tracks how often a member votes yes on bills that both parties’ majorities support. Across the 80 such votes in the current House, the rank correlation is 0.88 among Democrats and 0.88 among Republicans.

The median Freedom Caucus member voted yes on 53% of those bipartisan bills. Other Republicans: 99%. The Progressive Caucus sits lower than other Democrats too (88% vs 97%), but nowhere near as far.

One caution: the positions were estimated from these same votes, so this describes the axis rather than proving anything about it. The independent part is the caucus comparison, since the caucus lists never went into the model. This is also exactly the kind of group the synthetic Congress warned about: one that differs on a second dimension, where a one-dimensional model’s error bars miss.

So I fitted the two-dimensional Bayesian model to the current House too, to get error bars on both axes. On dimension 2, 30 of the 31 Freedom Caucus members have a 90% range lying entirely below the median of other Republicans. That isn’t automatic: only a third of the other Republicans do. Their ranges are also narrow (half as wide as other Republicans’), so the gap isn’t a few noisy members.

The second axis also changes the first. Among Republicans, the one-dimensional scale and DW-NOMINATE’s first dimension both largely are the bipartisan-bills pattern (rank correlation with the yes-rate -0.85 and -0.76). Once the model has a separate axis for it, its left-right scale barely relates to that pattern (-0.16), and agrees much less with DW-NOMINATE among Republicans (0.54, down from 0.89). The median Freedom Caucus member moves from the 93rd percentile of Republicans on the one-dimensional scale to the 66th on the two-dimensional left-right axis.

In other words, much of what puts them at the far end of a one-dimensional scale is voting no on bills both parties back. A caveat: a two-dimensional model doesn’t fix which way its axes point. I lined them up with logistic PCA’s map, so this split is one reading of the same positions, not the only one.

Polarisation since 1973

Finally I fitted every Congress from 1973 to 2025 separately and measured the gap between the party medians in “typical party widths”. It’s a scale-free measure, so different years can be compared.

In the House the gap grew from 1.9 party widths in 1973 to about 7 today. My series tracks DW-NOMINATE’s closely (correlation 0.98 in the House, 0.89 in the Senate), and so does the share of party-line votes taken straight from the raw data with no model at all. Since the early 2000s essentially no member is closer to the other party’s median than to their own.

The two models disagree about the 1970s: about 1 member in 5 overlapped the other party by my one-dimensional fit, but 1 in 20 by DW-NOMINATE. That era’s cross-party votes (notably Southern Democrats) ran partly along a second dimension, and a one-dimensional fit squeezes them onto left-right. It’s the same failure the synthetic Congress showed, appearing in real history.

What I’d tell someone running this analysis

1. Score within party. The party split is free. Report the 0.52, not the 0.97.
2. Build an answer key. A simulation with known positions is the only place a method can be graded exactly. DW-NOMINATE is a comparison, not the truth.
3. Beat the party rule. “Vote with your party” already predicts 93% of votes, so a model has to clear that.
4. Don’t trust error bars from a model that can’t represent the thing you’re measuring.
5. Report clusters with their stability. A clustering that changes when you resample isn’t a finding yet.

Data: Voteview (Lewis, Poole, Rosenthal, Boche, Rudkin & Sonnet), voteview.com. Caucus lists: Wikipedia, retrieved 2026-10-17; the Freedom Caucus doesn’t publish its roster, so that list covers publicly identified members. These are public officials’ public votes, described with the methods’ own neutral terms.