The argument goes that Labour will struggle to win key seats in parts of England with a left-wing leader. It will struggle even more, it is thought, if the party splits.
The current electoral system makes it difficult for Labour to win without a broad base of support. With the British electoral system, parties need broad support nationally in order to form a government. Labour needs to win votes in the south of England and among all social groups to be successful.
That is why Labour has been a social democratic party built on compromise. There is a real question of whether a Labour party led by Corbyn can build the support it needs for victory.
In Britain there are, in principle, two main constraints on a government. The first is the prospect of losing the next election. This forces the government to contemplate the impact of its policies on the electorate. The second is a strong opposition that challenges the government and offers alternatives.
If Labour is split and focused on internal conflicts (and potentially a leader more concerned with ideology rather than victory), then these constraints on the Conservative government disappear and the potential for it to implement radical policy becomes unconstrained.
With a left-wing Labour party, a Scotland dominated by the SNP and the potential of future boundary changes, the Conservatives are in a strong electoral position. They could find it easy to win elections for the foreseeable future. However, this electoral dominance is fraught with dangers for the party.
For one thing, there is a big question around the implications of Conservative domination for the political system and the process of governing in the UK. The Conservatives won the 2015 election with a very small proportion of the electorate and only 37% of the vote.
The party has already used its slim majority to push through radical changes in welfare policy and trade union reform. And as it pushes on with cuts, public services will under go more transformation.
The Conservatives risk alienating voters if they try to use a weak opposition to push through even more radical, unpopular policies.
Victories built on a small vote and excluding a large part of a disillusioned electorate will increasingly undermine the legitimacy of the system.
There is a danger that the Conservatives will build up considerable resentment unless they are prepared to consider fundamental constitutional reform. In this sense, a weak Labour party, when combined with a divided electorate, actually puts the Conservatives in a considerable bind.
The 2015 election has resulted in the voices of many UKIP and Green voters being excluded from parliament. A future long run of Conservative victories will further exacerbate their sense of political exclusion.
An outsider from the inside
What is clear about Corbyn’s victory is that it represents more evidence of the growing anti-establishment voice in Britain. People are not satisfied with politics as usual. But the paradox is that his victory allows the politics as usual to continue.
The evidence of a new politics is widespread. Millions voted for UKIP and the public have reacted passionately to the refugee crisis. There is concern over Cameron’s patronage in the House of Lords and widespread disillusionment with established institutions.
Corbyn’s election is part of this process. Yet, he is, in many ways, a child of the parliamentary system. Corbyn’s politics are steeped in party-led state socialism of the post-war era and not the radical new politics of the broad array of social movements that operate within the UK. This is perhaps best exemplified by how white, male and middle class his senior team has turned out to be.
At the same time, a long period of Conservative dominance – on a slim electoral base – will only exacerbate the alienation felt by many voters. It is difficult to see how the Conservatives can restore legitimacy without some process of constitutional reform.
Indeed, electoral reform would allow Labour to divide between its socialist and non-socialist wing, give representation to both UKIP and the Greens and create the need for governments that represented a wider range of voices. Corbyn’s election is part of the wider questioning of current politics – the danger is it does little to resolve it.