The Senate is gumming up the work of the Liberal government, slowing the process that turns bills into law because the government cannot reliably count on a majority of senators lining up behind it, according to an analysis of votes in the upper chamber.

But the numbers also show this isn't due to the independent senators named to the Red Chamber by Prime Minister Justin Trudeau. In fact, these independent senators have voted closely with the government — more often than the "Senate Liberals" cut loose from the party in 2014.

The Senate is currently divided into three groupings: Conservatives, Liberals and an Independent Senators Group (ISG). There are also a few non-affiliated senators, including Peter Harder, the government representative responsible for guiding the government's agenda through the Senate.

The Conservative senators form part of the party's parliamentary caucus, along with Conservative MPs from the House of Commons. But the Liberal senators were ejected from that caucus in 2014 by Trudeau, a move aimed at reducing partisanship in the upper chamber.

Though they still caucus together in the Senate, they no longer co-ordinate with their colleagues in the House.

The ISG is formed of senators who left their former Conservative or Liberal caucuses, as well as those put in the Senate by Trudeau as part of the government's pledge to appoint non-partisan senators nominated by an independent commission.

As the opposition in the Senate, the Conservatives have voted against the government's position the most often, siding with Harder in just 25 per cent of all 48 recorded votes held since Harder took office. (This includes votes on both government and non-government bills and motions.)

But the swing votes in the Senate have not been the gaggle of independents, but rather the Senate Liberals, who have voted with Harder only 78.5 per cent of the time.

The independents, by comparison, have been much more co-operative. Independents appointed by Trudeau's predecessors voted with Harder 88 per cent of the time, while independents named by the prime minister have stood with Harder in 94.5 per cent of recorded votes.

This makes Trudeau's independents — as a bloc — the most reliable votes that Harder can count upon in the Senate.

Senate Liberal swing votes

This bloc is not large enough for Harder to easily steer the government's legislation through the Senate.

With 98 senators — excluding Speaker George Furey and Jacques Demers, who has been away due to poor health — Harder needs 49 votes to pass legislation when all senators are in the chamber.

In addition to himself, Harder can count on the support of his deputy, Diane Bellemare, and government liaison Grant Mitchell. The independents named by Trudeau increase his vote total to 29.

Adding the six independent senators appointed by past prime ministers who frequently vote with the government bumps that number to 35 — still short of a majority.

So in order to pass legislation, Harder needs most of the votes from the 18 Liberals, making them the Senate's decisive swing votes.

Compliant House vs. rogue Senate

By the standards of the House of Commons, the Senate Liberals are downright unreliable.

While about 98 per cent of Liberal MPs vote with their government in the House at least 95 per cent of the time, not a single Senate Liberal has achieved that watermark in the current session.

According to an analysis conducted in February, even Nathaniel Erskine-Smith, the most frequently dissenting Liberal MP, voted with his government 87 per cent of the time. A full 15 of the 18 Senate Liberals have been less compliant.

A majority of senators have voted with Harder a majority of the time, but the rate of dissension demonstrates why no single vote in the Senate is a sure bet — particularly when compared to the House, where party discipline, whipped votes and the Liberal majority ensure success on any matter the government wants.

(A full breakdown of how senators have voted can be found at the bottom of this article.)

'Independent' senators?

Though the prime minister has touted his Senate-nomination process as non-partisan, it is clear that the senators who have been appointed by Trudeau are like-minded individuals.

Of the 26 independent senators appointed to the Senate by Trudeau, along with Harder, nine have sided with Harder in every recorded vote, two have abstained on one occasion and eight have voted in opposition only once.

That means just seven have voted differently from the government's representative on multiple occasions.

P.E.I. Senator Diane Griffin has been the independent most willing to oppose the government that appointed her, voting with Harder 83 per cent of the time.

The other Trudeau-appointed independent senators who have sided with the government in less than 90 per cent of votes were: Ontario Senator Frances Lankin, and Quebec Senators André Pratte and Marie-Françoise Mégie.

Still, their rate of dissent makes them more likely to vote with the Liberals' government representative in the Senate than the bulk of the actual Liberals in the Red Chamber.

The changes the prime minister has made to transform the Senate into a more independently minded chamber of sober second thought have certainly turned it into a more unpredictable place. But he likely didn't expect the Liberals in the Senate, rather than the independents, to be the biggest source of that unpredictability.