Currently only two leadership candidates go to a final vote, a rule set under Lord Hague’s leadership, but activists want any MP with the support of 20 colleagues to go through.
He compared the idea to Labour’s rule changes of 2015, when opening up its membership led to a surge in hard-left supporters and the election of Jeremy Corbyn, which he said left democracy “fundamentally weaker”.
Lord Hague, a former foreign secretary, said the change would help Mr Johnson, “who is currently thought to be more popular with the party members than with parliamentarians”.
But he warned it would put too much power in the hands of Tory activists, who he says “are often the first to point out that they are not remotely representative of society at large or even of their voters”.
He highlighted a call by Leave.EU, a hard Brexit campaign group, for its supporters to “flood” the Conservative Party to ensure a “true Brexiteer” like Mr Johnson becomes prime minister.
Lord Hague’s reform gave party members the deciding vote in a leadership contest for the first time.
He said he had hoped the rules would lead to the revival of the Conservative grassroots but had been proved “spectacularly wrong” after membership of the party halved to its current level of 124,000.
“A small membership is then at risk at any time of being swamped by a sudden influx of new recruits – the very thing that happened in Labour in 2015,” he said.
“Having not thought to include the three-month membership requirement in their own new rules and having all candidates put to the whole party, Labour’s former leaders inadvertently produced the leadership of Jeremy Corbyn, complete with extremism, antisemitism, divisiveness and the impossibility of removing him.
“The result of what might be thought of as a more perfect and open democracy in Labour is that British democracy as a whole is now fundamentally weaker, since there is currently no moderate, easily electable alternative to the government of the day.”
He also drew parallels with the US, where open primaries replaced the influence of senators and governors, leaving voters with a choice of Donald Trump or Hillary Clinton.
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