The Conservatives received a boost last week when Brexit party leader, Nigel Farage, announced he would not be standing candidates in Tory seats. But the advantage is not what it seems.

Brexit party candidates are still standing in most Labour-held seats, including those the Conservatives are targeting. This damages the prospects of Conservative challengers, who draw their support heavily from Leave voters, and are therefore more vulnerable to Brexit party competition than Labour incumbents, whose support comes predominantly from Remainers even in seats that voted heavily for Leave. Farage’s “country before party” initiative therefore looks more like an “incumbents before challengers” initiative – the party founded to shake up the establishment is helping both Conservative and Labour MPs keep their jobs.

Farage’s decision has broader implications. By standing down hundreds of candidates, Farage, who just weeks ago was threatening to campaign against Boris Johnson’s Brexit deal up and down the country, is tacitly endorsing it. As a result, we won’t see him on the nation’s TV screens railing against the Conservatives’ “betrayal of Brexit”. Many Leave voters tempted by the Brexit party, and who often have little trust in the Conservatives or their leader but much affection for Farage, will take the hint. Yet while a Farage endorsement will cement Leave support, it risks repelling Conservative Remainers by reinforcing their concerns that the Tory party is being taken over by extreme Brexiters.

The complicated effects of the Brexit party initiative illustrate a broader dilemma for the parties, one often overlooked by those arguing for local pacts to maximise the prospects of Leave or Remain candidates. Parties need to weigh the effects of such pacts on national reputations as well as local contests. The Liberal Democrats’ contortions over Canterbury candidates last week illustrated the headaches this can produce. Lib Dem candidate Tim Walker announced he was standing down to maximise the chances of the local Labour MP holding off her Conservative challenger. He was backed in this decision by the local party, but immediately overruled by the national leadership, who imposed a new candidate.

On the face of it, this behaviour seems bizarre. The Lib Dems are out of the running in Canterbury, so why would the national leadership antagonise local activists and boost Conservative prospects by insisting on standing a candidate? The answer lies on the broader electoral battlefield. Most Lib Dem targets are Conservative-held and usually Remain-leaning seats in suburbia and south England. Attracting wavering Conservative Remainers is crucial for Lib Dem prospects in such seats, and Jeremy Corbyn’s Labour is anathema to such voters. Hence local Lib-Lab pacts are off the table, even with strongly Remain Labour MPs, because the Liberal Democrats cannot afford to look like friends of Corbyn in their Conservative-held targets.

Yet rebuffing Labour too strongly also poses risks, because the Lib Dems also need tactical Labour voters in most of their target seats. The decision to veto local co-operation initiatives risks tarnishing the party’s appeal with Labour voters, who may be more reluctant to lend “stop Brexit” votes to a party that appears reluctant to reciprocate elsewhere. And even if the fuss over Canterbury is soon forgotten, continued expressions of opposition to a Corbyn-led government from Jo Swinson will make it harder for the party to portray itself as a friend to Labour voters in target seats.

Similar local v national dilemmas also arise for the three parties – the Greens, Plaid Cymru and the Liberal Democrats – who have agreed to co-operate under the “Unite to Remain” banner in 60 seats. This pact may reap fewer votes than past election results suggest. Many Green and Plaid Cymru voters are well to the left of the Lib Dems, and remain suspicious of the party in the wake of its former coalition with the Conservatives. They may opt to ignore their party’s endorsement and instead back Labour, or stay at home. Reciprocal suspicions exist among many more centrist Lib Dem voters about the Greens and Plaid Cymru. And these reputational effects that stretch beyond the seats where the pact operates will change the national image of the pact members in unpredictable ways.

What about Labour? They are the intended target of the Brexit party’s candidate strategy, though it may harm them less than intended, and they stand to lose from Lib Dem competition for Remain votes. They also face an uphill struggle in Scotland, where the SNP is seeking to squeeze Labour Remain voters to deliver a 2015-style Westminster landslide. Yet there may be some upside to these local weaknesses. Many wavering Remain voters dearly want to stop Brexit, yet do not want a radical Labour government. If both local competition patterns and national polling suggest a Labour majority is impossible, it may be easier to persuade such voters that backing Labour will deliver a weak, constrained and Brexit-focused Labour minority, not a majority that unleashes Corbynism. Sometimes local pacts do more harm than good nationally, and sometimes local weakness can be a national strength.

Robert Ford is professor of politics at the University of Manchester