I was originally going to write this as a comment to this diary by benamery21, but felt I needed more room to expand on my idea.
Indexing minimum wage to CPI, a seemingly great progressive idea, may actually be regressive. Unless you think a $4.08/hr minimum wage is progressive, you should think again about inflation indexing of the minimum wage. Here's why:
Assuming real GDP/capita and productivity are both increasing, and hours worked are not increasing, average wages must grow faster than inflation in order to maintain a constant labor share of income. Unless minimum wage grows at least as fast as the average wage, the minimum wage worker will have a decreasing relative standard of living. Thus, in a healthy economy, unless the minimum wage grows faster than inflation, the minimum wage worker will experience a declining relative standard of living.
I think this argument makes sense. The problem with the system we have now is the political intransigence that has prevented our respective governments from raising the nominal value as often as needed.
So here's my basic proposal: calculating based on the poverty level + median income.
For example: 120% of the poverty level + 20% of the median income.
The first ensures the minimum wage is always a livable wage. The second ensures some comfort without putting as much upward pressure on overall wages.
So for example, for a household with 1 working adult:
Let's say the poverty level is $10,000
And the median income is $30,000
120% x $10,000 + 20% x $30,000 = $18,000
$18,000 / 52 weeks / 40 hours = $8.65
So not much more than we have now, but this way, it only rises if the poverty level rises, or the incomes of a large number of Americans rises.
The political battles would switch over to what the percentages should be, rather than how to incrementally index the value or the nominal value.
In a thriving economy, where the median income is growing, the minimum wage would grow slower, but not relative to standards of living. Even if inflation drives costs up and in doing so pushes the poverty level up, a minimum wage worker would still be making more than they were after accounting for inflation.
If the median income were to increase from $30,000 to $40,000, and the poverty level from $10,000 to $15,000, the minimum wage would work out to $12.50. So a median income worker is earning $4.80 an hour more on average, but the minimum wage worker is only earning $4.00 more.
In a depressed economy, where the median income dropped from, say, $30,000 to $20,000, the minimum wage would only drop from $18000 to $16000, or drop by less than 1 dollar an hour.
In a severely depressed economy, where the median income is almost equal to the poverty level, the minimum wage would automatically work to keep wages in the livable range. The median income would never drop below 120% of the poverty line. This might suggest a lot of other things going wrong with the economy, but one can't expect the minimum wage to be the solution to all of the economic issues. At least this way, it offers a floor to how low wages can go.
On the political front, it allows progressives and conservatives to set ideological differences (Progressive might say 200% poverty/50% median, Conservatives might say 50% poverty/30% median), but the more extreme ends of the spectrum would no longer be politically viable.
I think a model like this avoids the main problems with indexing the minimum wage to something simple like inflation, and our current system of raising it incrementally through political action, or more often, inaction.
It upholds the progressive value of a minimum wage that is actually a livable wage, ensures our minimum wage workers are not left behind in a strong economy, and not callously driven to extreme poverty in a depressed one.
Disclaimer: I am not a trained economist, so I'm playing fast and loose with the macro theory. Further insight from people more in tune with the nuances is greatly encouraged.