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The larger Hillary Clinton’s polling margin over Donald Trump grows, the louder the question becomes: Is control of the House of Representatives really in play?

Among House strategists in both parties, the answer remains the same as it has been all year: not yet. Democrats must gain 30 seats to capture a majority. That requires sweeping nearly all Republican-held seats in which they nurse even small hopes of winning.

Yet the interplay between the presidential race and others on the ballot has made those small hopes bigger. So far, to the relief of Speaker Paul Ryan, pollsters don’t see evidence of a broad Democratic wave. Trump’s candidacy has veered so far outside traditional political norms that it hasn’t changed how voters regard most conventional Republicans.

Their prospects nevertheless remain connected, at least loosely. Robert Erikson, a Columbia University scholar of links between the presidential contest and down-ballot races, notes two competing influences. The coattails of popular White House candidates lift House candidates of their party by drawing like-minded voters to the polls. Because of party polarization, those backing Democratic presidential candidates typically back Democrats for the House and Senate, too.

But another subset of voters offsets that effect by, consciously or not, seeking balance. They back the dominant presidential contender but also the opposite party for the House to constrain the new chief executive.

Balancing occurs once voters decide that a presidential candidate is very likely to win. With prediction models pegging Clinton’s chances at 90 percent or more, that has happened. Balancing has already been priced into the polls, Erikson said.

“Between now and Election Day,” he said, “the major impact on the vote for Congress will be the coattails factor.”

As Clinton stretches her lead, she stands to gain some voters who pay less attention to distinctions and end up voting a straight Democratic ticket. Others will lean Republican for Congress but will tilt to Clinton because they can’t stomach Trump.

Using data from elections since 1948, Erikson estimates the coattail effect this way: Every percentage point added to a Clinton victory margin would add half a point to the average Democratic House candidate.

Districts: One problem for Democrats is that their House votes are distributed less efficiently than Republicans’. Urban residential patterns leave Democrats more densely concentrated in fewer, urban districts.

Gerrymandering in Republican-controlled states magnifies the problem. Thus in 2012, as President Barack Obama won re-election with 51 percent of the vote, Democratic congressional candidates took 50.6 percent of the vote but won just 46.2 percent of House seats.

A second problem is some entrenched Republican lawmakers in otherwise Democrat-friendly districts. Polarization elevates partisanship over incumbency as a factor in congressional election outcomes. But Democrats concede their inability to dislodge representatives such as Peter King of Long Island and Frank LoBiondo of southern New Jersey, both in the House for more than two decades.

Margin: Gary Jacobson of the University of California, San Diego, uses generic vote poll questions to predict House outcomes. In his calculation, which subtracts those who are undecided, voters now say by a margin of 53 percent to 47 percent that they want Democrats to control the House next year.

House Democrats need to stretch that edge to around 55-45 percent to come within range of a majority, he estimates. And to do that, they need a Clinton victory margin larger than the roughly 6-percentage-point polling margin in the current New York Times national average.

“If she wins by 10 points, Democrats have a shot at the House,” Jacobson said.

With Trump stalled at around 40 percent in the polls, and support for third-party candidates shrinking, it could happen.

Nearly everything would have to break the Democrats’ way, though. Of roughly three-dozen Republican-held seats where Democrats are within shouting distance, they’d need to win 30 of them.

David Wasserman of the Cook Political Report still envisions Democratic gains of no more than 20 seats. But even if Ryan retains his gavel, a collapse by Trump could nonetheless have implications for the Republican caucus and for the legislative prospects of a President Clinton.

In 2012, Obama carried only 17 districts won by House Republicans. This year, Wasserman said, Clinton may carry three times that many.

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