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Democrats won several important races last night — chief among them Bill de Blasio’s runaway win in the New York mayoral race and Terry McAuliffe’s victory in the Virginia governor’s race.  There is no question that winning is better than losing. But there are some cautionary notes for Democrats too.  Here are 4 takeaways:

1) In New York City, de Blasio may govern as a liberal, but that’s not necessarily what every New Yorker wants.  We shouldn’t treat elections as policy referenda.  It’s not clear most voters have enough incentive to learn details about the candidates’ platforms and vote accordingly.  According to new research by political scientists Douglas Arnold and Nicholas Carnes, New Yorkers evaluate their mayors based quite a bit on performance — is the economy humming along, is crime down, etc.  Perhaps the best indicator of why this was a good year for a Democrat is New Yorkers’ middling assessments of Michael Bloomberg’s performance.  In a recent Marist poll, only 47% approved of the job Bloomberg was doing, 49% approved of the direction the city was heading, and 64% wanted to move the city in a different direction.  And in a cautionary note for de Blasio, nearly 3 in 10 New Yorkers (29%) already say that he is too liberal.  In sum, I think there’s reason for de Blasio to proceed cautiously with his “progressive experiment.”

2) The Virginia and New Jersey gubernatorial races don’t consistently predict the next midterm elections.  The University of Virginia’s Kyle Kondik and Larry Sabato ran through the numbers here.  Certainly McAuliffe’s win, which was narrower than the polls predicted, doesn’t seem to presage Democratic wave in 2014.  In general, these off-year elections are at least as much noise as signal when it comes to predicting midterms — featuring idiosyncratic states, electorates, and candidates, as well as a national agenda that could be quite different than it is a year later.

3) Chris Christie’s victory helps make him a more viable Republican presidential candidate.  Period.  Yes, he will face challenges if he chooses to run.  But there is no question that winning reelection so handily helps his cause, relative to a narrower victory.  And this should concern Democrats. There is some evidence that moderate candidates do better in presidential elections — and anything that makes it more likely that the GOP nominates someone like Christie as opposed to someone like Ted Cruz isn’t good for Democrats.  In short, last night made it more, not less, likely that Christie could be the nominee.  And, relative to someone like Cruz, having Christie as the nominee makes it more likely that the GOP can retake the White House in 2016.

4) The lesson that the GOP will likely learn from Christie’s victory and Cuccinelli’s defeat is that it needs to put forward relatively moderate candidates.   You can already see this notion taking shape in conventional wisdom, if The Fix is any indication.  And you can see this notion taking hold in the GOP itself — in the outcome of last night’s Alabama primary election, in Cruz’s recent pledge not to campaign against Senate incumbents, etc.  If the GOP can successfully nominate relative moderates — and there’s certainly no guarantee they will in every relevant district or state in 2014 — then this won’t help Democrats either.  (Note I’m saying “relative moderate.” Whether any candidate is a true moderate is a different question.)  This won’t help Democrats in 2016 either.  Commentators often overestimate the willingness of parties to roll the dice with a presidential candidate from the fringes of the party.  But in basically every competitive presidential primary since 1988, the GOP has nominated a relative moderate from the field, and 2012 was no exception.  Spending 8 years out of the White House only makes it more likely they will nominate a (relative) moderate in 2016.  Last night may have pushed Republicans further in this direction.