Having fired the starting gun for the general election, Theresa May has started to receive unsolicited advice about policy ideas that she could campaign on.

Baroness Altmann, the former pensions minister, says that most people “don’t realise that 20% tax relief gives them a 25% Government bonus on their pension contributions, while higher rate taxpayers get 40% tax relief, which is a 66% bonus”. She wants Mrs May’s pitch to voters to include “a 33% Government bonus being offered to everyone”.

Does 20% upfront tax relief really amount to a 25% “Government bonus”? Sure, each £100 contributed to a pension only costs a basic rate taxpayer £80 of disposable income. But that’s not the end of the story. A second helping of tax is due on three quarters of the amount withdrawn in retirement, which would not be the case if the £80 had been saved outside a pension. If politicians want to call tax deferral a “bonus”, they must acknowledge that it arrives hand-in-hand with a penalty.

For an employee pension contribution by a basic rate taxpayer, the net end-to-end reward for pension saving will only be as high as 25% if the whole amount can be withdrawn tax-free. The first tranche of pension saving that someone does should be this tax-favoured: as long as the personal allowance remains above the full New State Pension, some theoretically taxable private pension income will in practice be untaxed.

Beyond that, once taxes have partly cancelled out the top-up, a basic rate taxpayer can expect to get back £85 in retirement for each £80 saved from post-tax income – ignoring any investment returns, which could also be achieved outside pensions. That’s a bonus of 6.25%, not 25%. Baroness Altmann’s “33%” proposal would increase this to a little over 13%. (Higher “bonuses” are available, in the form of National Insurance savings, if contributions are paid via an employer.)

Putting presentation to one side, how would a “33% Government bonus for everyone” be implemented?

Currently, employees pay no upfront benefit-in-kind tax on employer pension contributions; this is equivalent to giving them tax relief at their marginal rate, the treatment which Baroness Altmann dislikes. Say an employer pays £1,000 into a 40% taxpayer’s defined contribution pension. Would this first of all be subject to 40% tax (reducing it to £600) and then receive a 33% top-up (increasing it to £798)?

Further questions follow from this. If employer pension contributions were taxable, would their value help determine what tax band someone is in? How would employer-financed defined benefit accrual be valued for tax purposes, and how would the net tax due from 40% taxpayers in these schemes be collected – from their pay packets or by making the scheme pay the tax and reduce the member’s benefits to meet the cost? Quickly cobbling a policy like this together ahead of an election campaign makes it less likely that these details would be thought through.

Mrs May has hired Sir Lynton Crosby to run her campaign. Prior to the 2015 election, Sir Lynton reportedly told David Cameron that he needed to “scrape the barnacles off the boat” – ie to shed extraneous messages and focus on core election-winning themes. Whatever the Conservatives might consider doing in Government, a messy-to-implement and difficult-to-communicate pensions tax overhaul might look like the sort of barnacle that could impede their electoral voyage – especially if they fear that prospective losers would take more notice than the winners.