I still think it's circular because it's not making a qualitative distinction between different kinds of prices.

The simplest social definition of inflation is that it decreases the choices available to participants in the economy.

This means not all prices are equal. If food becomes 50% more expensive, I have little or no choice but to buy it. (Assuming I'm on a standard and not on a luxury diet.) That means my choices decrease - I have less money to spend on non-essentials, and I have no flexibility in this.

I guess economists would wiggle out of this one by pointing out that, unless price rises happen in non-substitutable staples, people can always switch to other foodstuffs.

If there are Giffen Goods in the economy, of course, that is not the case.

But I think however you construct it (even if you do it in what you'd call a "socially sensible way") the GDP Deflator and the Real GDP are not directly measurable, but have to be constructed from the details of the Nominal GDP, which is measurable (at least in principle).

I guess this is another case of an economist going and saying "look here: nominal GDP growth consists of two components: real GDP growth and inflation", and people going "ooh, ahh", and after giving the economist his Nobel price going "but how do you calculate real GDP and inflation?". And after much debating turning to the statisticians and saying "guys, here's the data on all the goods and services traded over time, with amounts and prices". Please figure out a way to calculate the Real GDP and the GDP Deflator.

By the way, there's the following juicy quotation from Keynes:

That the units, in terms of which economists commonly work, are unsatisfactory can be illustrated by the concepts of the national dividend, the stock of real capital and the general price-level:

...

Thirdly, the well-known, but unavoidable, element of vagueness which admittedly attends the concept of the general price-level makes this term very unsatisfactory for the purposes of causal analysis, which ought to be exact.

Nevertheless these difficulties are rightly regarded as 'conundrums'. They are 'purely theoretical' in the sense that they never perplex, or indeed enter in any way into, business decisions and have no relevance to the causal sequence of economic events, which are clear-cut and determinate in spite of the quantitative indeterminacy of these concepts. It is natural, therefore, to conclude that they not only lack precision but are unnecessary. Obviously our quantitative analysis must be expressed without using any quantitatively vague expressions. And, indeed, as soon as one makes the attempt, it becomes clear, as I hope to show, that one can get on much better without them.

The fact that two incommensurable collections of miscellaneous objects cannot in themselves provide the material for quantitative analysis need not, of course, prevent us from making approximate statistical comparisons, depending on some broad element of judgement rather than of strict calculation, which may possess significance and validity within certain limits.

But the proper place for such things as net real output and the general level of prices lies within the field of historical and statistical description, and their purpose should be to satisfy historical or social curiosity, a purpose for which perfect precision—such as our causal analysis requires, whether or not our knowledge of the actual values of the relevant quantities is complete or exact—is neither usual nor necessary. To say that net output to-day is greater, but the price-level lower, than ten years ago or one year ago, is a proposition of a similar character to the statement that Queen Victoria was a better Queen but not a happier woman than Queen Elizabeth—a proposition not without meaning and not without interest, but unsuitable material for the differential calculus. Our precision will be a mock precision if we try to use such partly vague and non-quantitative concepts as the basis of our quantitative analysis.

— John M. Keynes in The General Theory of Employment, Interest and Money

We have met the enemy, and it is us — Pogo