Douglas Elmendorf, director of the Congressional Budget Office (CBO), right, speaks during a House Financial Services Committee hearing on the Ex-Im Bank reauthorization with Fred Hochberg, chairman and president of the U.S. Export-Import (Ex-Im) Bank, from right, Osvaldo Gratacos, inspector general of the Ex-Im Bank, and Mathew Scire, director of financial markets and community investment at the Government Accountability Office (GAO), in Washington, D.C., U.S., on Wednesday, June 25, 2014. (Andrew Harrer/Bloomberg)

BY ITS nature, the legislative process in Washington is political and partisan, and hence prone to error, bias and outright propaganda. The antidote is a common set of facts and objective analysis, provided by a source that everyone in Congress recognizes as an honest broker of information. For the past 40 years, that honest broker has been the Congressional Budget Office, which is required by law to provide lawmakers with cost estimates and forecasts of government programs. The CBO’s budgetary impact “scores” are the gold standard against which politicians’ fiscal promises are measured.

And so one of the most important decisions facing the new bicameral Republican majority will be what to do when the term of current CBO director Douglas Elmendorf expires on Jan. 3. The new congressional budget committees’ leadership under House Speaker John A. Boehner (R-Ohio) and Senate majority leader-to-be Mitch McConnell (R-Ky.) will be sorely tempted — and, by some in their party, heavily pressured — to replace Mr. Elmendorf with someone more amenable to GOP doctrine, perhaps an economist willing to mark down the fiscal impact of tax cuts by counting the projected economic growth they supposedly create.

This would be a terrible mistake, one that would go a long way to discrediting the GOP’s promise, in the 2014 campaign, to be the party of making Washington work. Enough institutions in the capital have been contaminated by polarization already, without adding the CBO to the list. If Republicans really wanted to demonstrate their non-ideological bona fides, there would be no better way to do it than to retain Mr. Elmendorf for a new four-year term. (He took over in 2009 when then-director Peter Orszag left to join the Obama administration and was reappointed in 2011.)

Mr. Elmendorf has a well-earned reputation for refusing to tell policymakers what they want to hear; in 2009, for example, he publicly declared that an early draft of Obamacare would increase, not decrease, health-care costs, thus forcing the president and his congressional allies back to the drawing board. This makes it sadly ironic that some on the right now are suggesting that Mr. Elmendorf is a “Gruber ally” — as in Jonathan Gruber, the Massachusetts Institute of Technology economist and Obamacare adviser who is under fire for comments suggesting that the administration shaped the legislation deceptively to achieve a favorable CBO “score.”

Several prominent Republican economists, including former Mitt Romney adviser N. Gregory Mankiw, have suggested offering Mr. Elmendorf another term. Congress would be well-served if he stayed. Should the new majority party decide to make a change, there is no shortage of potential honest brokers on the GOP bench. Mr. Mankiw himself is one, as is Katherine Baicker, a former George W. Bush White House economist who is an expert on health-care economics at Harvard.

The important thing is that the GOP treats this appointment as a way to shore up its reputation for governance, not to shore up its political base. There will be plenty of other opportunities for that.