Yea sure, market value "correlates" to a price in an assumed hypothetical transaction.
Price is actually something that has transpired, involved an exchange of assets, where I believe we may assume that whatever assets are used gets translated into a monetary equivalent. So, if Mr X buys a house from Mr Y for 300 pigs, 4 horses and 30 young milk cows, that later could be called the price, but for financial purposes we would determine the market value of the animals in dollars, perhaps discounting for some issue or another such as sale fees; then we could use that market value for the market value of the transaction. Of course in each appraisal their is most likley error, or if you prefer, - the potential for error. So, in this case, we would be compounding any errors. So it might better if Mr X would sells his animals first and use that money for the house transaction. Except, of course, if maybe Mr. X thinks he has a chance of fooling Mr Y that the animals are worth significantly more that what they really are. But, then if Mr. Y buys into that, he cannot be considered knowledgeable, so the appraisal may turn out worse than expected because the appraiser may decide to punish Mr X for cheating and Mr. Y for being an idiot, which USPAP does not say much about in terms of exactly how an appraiser should handle such a situation, - and who is going to think the appraisers is up to no good anyway (he is not gaining anything financially)? Yep, it's a risk for Mr. X to not sell the animals, and a risk to sell them. We can talk about risks for Mr. Y, but I will leave that as exercise for the reader.
Market Value is the price in a hypothetical transaction defined by certain parameters and conditions..
Some definitions of Market Value say it is the most probable price. However, they fail to define "most probable price" correctly. The Dictionary of Real Estate Appraisal has
"most probable selling price: The price at which a property would most probably sell if exposed ..."
But that is completely circular. Now they still need to define "most probably."
Now Mr. Hillborn you are a mathematician, and you should be aware that "most probably" and "probably" can have various definitions. Now suppose I have a hypothetical event with 4 outcomes for the seller: A, B, C and D. A= not sell @ probability = 1%, B=sell for $100M @ probability=45%, C= get sued and lose $10M @probability = 4%, D= Sell for $50M profit probability @ 50%. What is the most probable value? Most mathematicians would say 0 x 0.01 + 100M x 0.45 + -10M x 0.04 + 50M x 0.50 = $69,600, using weighted average. But of course probability of actually getting $69,600 is 0. It will never happen by definition. The most probable outcome is actually D at 50%.
So, you might say the example is unrealistic in real estate. I would argue that it is not. We have many buyers who tend to fall into different preference and requirement categories. Some groups of buyers will pay much more for certain properties and some groups significantly less. If you want to predict the price a property would sell at at any particular time, as a sales broker, then you would first look very closeley at the market to see what kinds of buyers are present. Actually, one can argue this is something the appraisers should do as well - he should observe the market and uncover any important market conditions.
Thus, I would, anyone defining Market Value on the bases of "most probable" sale price, needs to define what they mean by "probable." and provide a protocol for determing whether a price is "most probable".