In a world of descriptivist dictionaries, how is linguistic relativism avoided in discussions?

“If you wish to converse with me, define your terms.”
—Voltaire

During discussions and debates, especially those of a more academic or technical nature, it is important to establish agreed upon definitions for terms. The reason we don't implicitly take the dictionary definition is because most modern dictionary definitions are descriptive, and "common usage" doesn't always map on perfectly to everyone's personal usage.

Given the following example, what prevents people from getting away with a relativistic kind of, "Well, that's not what I mean by X" response?

Richard: What a sunny day!
Gina: No, it isn't. Quite the opposite, in fact.
Richard: Yes, it is. The sun's out in its full glory and there are no clouds in sight.
Gina: Oh, I see. Well, that's not what I mean by "sunny". To me, "sunny" describes horrific torrential storms accompanied by sweeping floods.

In other words, to what extent can the personal usage of a word deviate from the "common" usage in a descriptive world.

The Swiss linguist Ferdinand de Saussure understood language as a social contract:

Language is not purely linguistic—it is enabled and reinforced by social conventions of use which are and have been transmitted from mouth to ear and from one generation of speakers to another. Language is an ongoing contract within a speech community which endures and is relatively resistent to change; even if this relative stability cannot be explained naturalistically, it supposes an inertial effect of shared investment in a tradition that an arbitrary system of signs considered on its own cannot account for. This receptive stance and acknowledged passivity of the language user before the sign removes any remnant of voluntariam from language, considering that historically sedimented social preactice largely constrains individual free choice in language use. — Beata Stawarska, Saussure’s Philosophy of Language as Phenomenology, 2015.

The inertial force inherent in language assures that change is not generally subject to individual whim but occurs in increments across time. The word sunny, for instance, emerged in English in the early 14th c. meaning, unsurprisingly, ‘full of sun’. This means that 14th c. speakers first heard the word sunny, found it apt and useful, and agreed to use it themselves and pass it on to their children.

As one can infer from your quote from Voltaire, the basis of a conversation — even a banal one about the weather — is that the speakers generally agree on the meanings of words in particular contexts. If Gina wishes to assign a meaning polar opposite to the one established some seven centuries ago, she is violating this social contract and will likely pay a social price. Not only will she be constantly explaining herself, but she will be dismissed as excruciatingly annoying.

Unless Gina is, say, a popular novelist, an academic with a large list of publications, or a political figure especially noted for eloquence, her individual chances of any lasting influence on the language approach zero: those whose language is mirrored in dictionaries are educated elites. Thus the degree to which a dictionary is descriptive is limited by its aspiration to be a standard reference work.

Take the pronunciation of the word almond. The New English Dictionary (1888), predecessor of the OED, gives a single pronunciation, followed still today by Collins online for British pronunciation: \ˈɑːmənd. For current American pronunciation, however, there are eight:

ˈɑmənd ; äˈmənd; also ˈæmˈənd & ælmənd; amˈənd & alˈmənd; ˈɔlmənd ; ôlˈmənd

Not only are there variances in the first vowel, but whether the l is pronounced at all.

Merriam Webster gives only four variants:

\ ˈä-mənd , ˈa- , ˈäl- , ˈal- \

And Random House only three:

ah-muh nd, am-uh nd; spelling pronunciation al-muh nd

The remark that pronouncing the l in almond is a spelling pronunciation is an alert that the traditional way to pronounce the word is without the l. Yet more and more speakers, especially younger Americans, are pronouncing the l in words like balm, calm, psalm, and almond. A purely prescriptive dictionary would simply give the traditional pronunciation of the NED as the single acceptable pronunciation for North America and be done with it.

Collins is by far the most descriptive, and while no dictionary gives preference to pronouncing the l, only Random House points out its somewhat suspect nature. Contrast this to falcon, which most everyone on both sides of the Atlantic now pronounce the l while the traditional spelling is relegated to last place in the list.

You could perform semantic tests on various dictionaries as well. How many, for instance, allow the adjective unique to be compared (This sofa is the most unique), which would indicate a more descriptive approach, or condemn or ignore it prescriptively?

Yet such questions are mostly peripheral. There is no rigid dichotomy of prescriptivism writ in stone battling a descriptivist chaos. As de Saussure suggests, the social contract of language is remarkably durable.