(CNN) In the wake of the divisive Brett Kavanaugh hearings, Chief Justice John Roberts on Tuesday tried to assure the public that the US Supreme Court serves the whole country, not one political party over another, and that it is committed to collegiality.

Yet, irrespective of what is happening in the political branches, America's highest court is deeply split along ideological and political lines, and Roberts sometimes fosters that divide.

"Those of us on the court know that the best way to do our job is to work together in a collegial way," Roberts said at the University of Minnesota Law School. "I am not talking about mere civility, although that helps. I am instead talking about a shared commitment to a genuine exchange of ideas and views through each step of the decision process. We need to know at each step that we are in this together."

That message is sometimes belied by the court's rulings and by personal tensions among the nine. In the most recently completed term, October 2017 to June 2018, many major rulings broke along 5-4 lines, with the five conservatives led by Roberts in control and the four liberals in dissent. The five on the right were appointed by Republican presidents, the four on the left by Democratic presidents.

The chief justice wrote for the narrow majority in the incendiary case of Trump v. Hawaii, upholding the administration's travel restrictions on people from mostly Muslim countries. The same five conservatives also voted together, over protests from the four liberals, to reverse a four-decade court precedent involving non-member fees for labor union collective bargaining.

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