Here is one of the problems in retirement planning: you can go along for years, faithfully using retirement calculators, re-balancing your stock market investments, reading your estimated social security payouts, just sure you are on track and – well, poof! – the rules of the game can change in an instant.

And, apparently, the United States government can do it too.

This brings us to the case of something called chained CPI, the vaguely off-sounding idea (chains anyone?) that budget hawks claim would save an estimated $112bn over the next decade. Chained CPI – that's short, by the way, for chained consumer price index – works by assuming we adjust to inflation not by spending more money, but by changing our behavior. So let's say you're wheeling your shopping cart at the Piggly Wiggly. If the price of filet mignon goes up, most of us will take a look at a cheaper cut of meat, like chicken.

The government is interested in the cost of what goes in your shopping cart, because that's how it knows whether prices are going up and down. It's also how it knows whether it should raise social security payments.

The idea is to stop linking social security to plain old prices and instead link them to a longer chain of consumer prices – not just what you are buying, but what you could buy. You could economize by buying vegetables instead of meat; you could buy generic; you could try to stretch your shopping dollar. And if you do, then that means that the government wouldn't need to give you as much money in your social security payment.

Republicans support the concept. Needless to say, the corporate titans behind the deficit-obsessed Fix the Debt campaign think it's a great idea, because it would limit how much social security payments could rise. Even the White House has signaled it could potentially be one of the compromises offered up as a way of ending the budget standoff between Democrats and Republicans.

As for the rest of us? Well, if you think getting less money than planned is a great idea, you're probably for it. As you can guess, that's not a large group of people. A recent McClatchy-Marist poll discovered that 60% of us would rather see taxes go up than see social security checks shrink.

So let's take a look at what's unfair about using chained CPI.

Here's one thing: chained CPI intimates that grandma and grandpa have been getting away with something. Your boss isn't giving you a pay increase, so why should the old folks get one? Proponents of chained CPI and other cuts in social safety-net spending on the elderly routinely pit them against the young 'uns, pointing out that so much money is not being spent on things like education because the oldsters won't take a financial hit. After all, it was 81-year-old senator Alan Simpson – he of the Simpson Bowles deficit cutting commission – who once described Social Security as "a milk cow with 310m tits."

Those who like the idea of using chained CPI argue that it would only cause a small decrease in payments, maybe one-third of 1% over a year. As an example, if chained CPI had been in effect when social security recipients received their 2013 increase, the average retired senior – who receives $1,262 a month – would have lost about $30 over the next year. That wouldn't even pay for one supermarket trip.

Yet this is the kind of thing that adds up. If you calculate that rate of decrease over a couple of decades, you're talking serious money. If someone collects benefits over 30 years, using chained CPI would cut their benefits by nine percent, according to the Center for Economic and Policy Research. That's one week's worth of food every month if you are an 80 year-old single woman, the National Women's Law Center says.

This is the moment where you might want to remember that chained CPI – in common with social security – has a female problem, that Simpson's infamous "tit" slip was aimed the National Older Women's League, an organization that represents and lobbies on behalf of elderly women.

By the age of 62, women make up 56% of Social Security beneficiaries, a number that will grow to almost two-thirds of recipients by age 85. Women, after all, live longer than men. Moreover, they are more reliant on social security than men to keep them out of poverty which is why AARP recently entitled a blog post on the subject "Social Security Benefit Cuts Would Have a Terrible, Horrible, No Good Impact on Women."

Finally, there is this: at least one alternative formula suggests that those over 65, instead of taking more than their fair share, are already getting the shaft. It's called called the CPI-E – that's "E" as in elderly. This formulation has it that the elderly deserve not a social security increase cut, but a raise.

The elderly, it turns out, are not flexible shoppers, eager to swap one good for another. They can't. They spend a disproportionate share of their money on medical services, an area where substitution is not often an option – unless your idea of a civilized solution is telling people to forego medications and replace their hearing aids with ear trumpets.

What makes this all so difficult is that there is a very simple solution to the supposed social security crisis, one that would ensure its future for many years to come: lifting the payroll tax cap. Right now, earnings above $113,700 are not taxed for social security. Tax them, and social security – using the current cost-of-living formula – will remain funded at just under 85% for next 75 years.

So why aren't we talking about that?