"If you're going to say something radical, make sure you wear a suit". This is the solitary piece of advice Alex Salmond's grandfather is said to have sent him packing with as he started his career in politics thirty years ago.

As party conference season draws to an end, it's this advice which separates the two main parties in British politics, and defines their current trajectory. One side gets it, the other ignores it.

It isn't really, of course, a line about what constitutes proper dress - or at least not just. What Salmond's grandfather meant was simple: if people can pigeonhole you, they will – so don't let them. Confound expectations.

It remains as relevant as ever. Unpack why and you get to three truths that most pollsters will tell you define the ways voters engage with politics: they consume it in very small quantities, largely through TV and newspapers; they make their mind up quickly; and, most crucial of all, they filter what they see back through the lens of what they already think. If you sound and look how people expect you to, they will box you in as that, even if what you're saying is eminently sensible. So much is not about what is being said, but who is saying it.

This is difficult to absorb when most political discussion is still wedded to the idea of a rational-actor electorate. But the reality is most normal people respond to signals not details (and abnormal people in fact: most of those who read this article and tweet me furiously about it will only have bothered reading the headline and top line).

Thus a huge part of electoral politics is challenging prejudices people have about you. In this contest advantage accrues to those who can do unexpected things; the counter-intuitive. So, for instance, only a party that can convincingly present as moderate earns the right to govern as radical.

This is ultimately the fatal mistake made by the many people – including myself – who wrongly thought Ed Miliband had a shot at Number 10. Because he never ruthlessly and publicly dealt with Labour's weaknesses, particularly spending and welfare, his broader agenda never got a hearing. James Morris argues Miliband's early years spent talking about “too far too fast”, however economically justified, just hardened for voters their own pre-existing prejudices: that Labour wanted to spend more and can't be trusted with tough decisions. Later, Miliband just switched the subject. As a result, BritainThinks found that even when he said things that polled well, voters simply asked “yes but where's the money coming from?” in a way they never did of the Conservatives.

Which brings us back to this year's party conferences.

The Conservatives spent most of their time in Manchester, as they have since May, playing to their strengths while happily, ruthlessly and publicly attempting to deal with their weaknesses among undecided voters. For “party of the rich”, see the living wage and overtures on “the workers party”; for “the nasty party” see Cameron's paeans to equality. How substantial this in practice is irrelevant, in the short term at least. It was all clipped for the news for the same reason it will have cut through with floating voters: because it's counter-intuitive. It buys them cover to be quietly radical and, in many areas, push a traditional free-market agenda Michael Howard would never have got away with.

Labour badly needs to learn this skill: presenting as moderate, governing as radical. At the moment it is adept at precisely the opposite. Windy socialist rhetoric is cranked up only to be accompanied by fairly conventional social democratic ideas. An economic policy largely the same as Ed Balls’ sent the conference hall into raptures because it was wrapped in the crotchety language of anti-austerity.

This is the surest sign of a movement in love with the sound of its own voice. Everything it did will have entrenched voters’ prejudices about them, wittingly or not. To be fair, most damningly of all, it seemed designed precisely for that purpose. Every signal was aimed at pleasing the already converted and reaffirming their virtue. If there was any talk of persuasion, it only showed through in a desire to lecture the public: “busting myths”, “nailing the lie” and so on. Not an ounce of self-reflection, or an understanding that these rights have to be earned.

To be fair, the frenzy among activists was been whipped up largely in response to a half justified grievance: that New Labour managed to be seen as moderate but didn't exploit it by governing radically enough, as the Conservatives are now, particularly when it came to political economy.

But the fact remains: Labour will not get the chance to change the country again unless it re-learns what Alex Salmond's grandfather taught him. It will not even get a hearing until it is willing to confound perceptions of it among Conservative voters in particular, as the Tories have learnt to do. Why does it deserve one?

The reason this hasn't been done is that it's not easy. It doesn't mean aping every last detail of Conservative policy – but it does mean moving closer to the small-c conservative values that run through the population of this country outside its big cities: prudence, fairness as opportunity not just outcome, quiet patriotism, contribution. At the moment the party is a world away: obsessed with an arid Keynsianism, infatuated with ideas of entitlement and embarrassed about national identity.

The change here has to run deep; it has to be more than finding the most temperate words in a thesaurus. The challenge is to renew the party's politics in a way that intrinsically deals with its weaknesses, but leaves it with a prospectus bold enough to change the country. It has to look, over and over again, like it genuinely cares about things voters don't expect it to: the deficit, waste, unfairness in the welfare system; the middle as well as the bottom, as well as being comfortable with technology and innovation. Otherwise it will never be able to broach a conversation about inequality, reforming the economy so it works in the interests of the many, or tackling vested interests. And British politics will remain what it is today: a non-competitive sport.