Solution 1:

Yes, majoritively is a word. As one of our resident professional linguists so succinctly put it:

If you use the word when speaking English, then it is an English word.

Now that that’s out of the way, what are we to make of the word majoritively? To start with, it comes from applying two common, productive suffixes to the existing word majority:

  1. -ive converts a noun into a adjective or another noun
  2. -ly converts an adjective into an adverb or a noun into an adjective

The second of those is incredibly productive; the first, somewhat less so, although as ‑ative it is fairly lively — just perhaps not quite so much as ‑ize is.

The OED tells us this about -ive:

-ive, suffix, forming adjs. (and sbs.)

Formerly also ‑if, ‑ife; a. Fr. ‑if, fem. ‑ive (= It., Sp. -ivo) :– L. īv-us, a suffix added to the ppl. stem of verbs,as in act-īvus active, pass-īvus passive, nātīv-us of inborn kind; sometimes to the pres. stem, as cad-īvus falling, andto sbs. as tempest-īvus seasonable. Few of these words came down in OF., e.g. naïf, naïve :– L. nātīv-um; but the suffix is largely used in the modern Romanic langs., and in Eng., to adapt L. words in ‑īvus, or form words on L. analogies, with the sense ‘having a tendency to, having the nature, character, or quality of, given to (some action)’. The meaning differs from that of ppl. adjs. in ‑ing, ‑ant, ‑ent, in implying a permanent or habitual quality or tendency: cf. ACTING, ACTIVE, ATTRACTING, ATTRACTIVE, COHERENT, COHESIVE, CONSEQUENT, CONSECUTIVE. From their derivation, the great majority of these end in ‑sive and ‑tive, and of these about one half in ‑ATIVE, which tends consequently to become a living suffix, as in talk-ative, etc. A few are formed immediately on the vb. stem, esp. where this ends in s (c) or t, thus easily passing muster among those formed on the ppl. stem; such are amusive,coercive, conducive, crescive, forcive,piercive, adaptive, adoptive, denotive, humective; a few are from sbs., as massive. In costive, the ‑ive is not a suffix.

Already in L. many of these adjs. were used subst.; this precedent is freely followed in the mod. langs. and in English: e.g. adjective, captive, derivative, expletive, explosive,fugitive, indicative, incentive, invective,locomotive, missive, native, nominative,prerogative, sedative, subjunctive.

In some words the final consonant of OF. ‑if, from ‑īvus, was lost in ME., leaving in mod.Eng. -Y: e.g. hasty,jolly, tardy.

Adverbs from adjs. in -ive are formed in ‑IVELY; abstract sbs. in ‑iveness and ‑IVITY (F. ‑iveté, ‑ivité, L. ‑īvitāt-em), as in activity, conductivity, resistivity, and similar terms; also spec. (see quot. 1895).

I’m a bit surprised you went for majoritively rather than majoritatively, in that ‑ative tends to be the “living” (read: productive) version as explained above.

It’s so productive, it has its own entry:

‑ative,

ad. F. ‑atif, ‑ative, L. ‑ātīvus, consisting of adj. suffix ‑īvus (see ‑IVE) appended to ppl. stems in ‑āt- of vbs. in ‑āre, e.g. dēmonstrāre to point out, dēmonstrāt-īvus ‘having the attribute or habit of pointing out, tending to point out.’ Only a few were used in Latin, but the analogy is extensively followed in the modern languages. In the majority of instances, as in demonstrate, demonstrative, adjs. in ‑ative belong to vbs. in ‑ate; cases like represent, ‑ative, affirm, ‑ative, figure, figurative, in which the Eng. vb. represents (through Fr.) the present stem of the Latin, have afforded a formal analogy for talk, talk-ative.

A few adjs. of this class are moreover formed directly from sbs. in ‑TY, as if from an intervening verb in ‑tate, which does not exist; e.g. AUTHORITY, (*authoritate), authoritative; so qualitative, quantitative.

That’s why I was somewhat surprised that you didn’t just go from majority straight into majoritatively. Some people do. In fact, all these can be found in print:

  • majoritive > majoritively
  • majoritative > majoritatively

We can tell from the definitions of the suffixes what these words MUST mean.

There are only a few dozen instances of each found in Google Books, so it is not as though these were especially common words. Even so, most citations are found in recent publications; they seem to have gained some traction in the 21st century.

I cannot say why that might be, but I will note that many books no longer go through the rigorous redaction process of draft, review, rewrite, copyedit, and proofread; it is possible that some of these might have been more felicitously phrased if they’d had a competent copyeditor to smooth out the wording.

In most instances, majoritively and majoritatively are used purely as synonyms for the simpler mostly. However, in some cases, they take on a different nuance because they are specifically talking about some sort of majority being involved.

  • The past and the future depend, majoritively, on sensations from physical stimuli that deal with substance, content and contest of the physical situation, . . . [The Forbidden Gift, Anttarr, 2007]

  • Are the trammels of a third-rate, majoritively non-Christian, non-Muslim South-East Asian state not of the utmost inconsequence? [Perfect Hostage: A Life of Aung San Suu Kyi, Burma's Prisoner of Conscience, Justin Wintle, 2007]

  • Level A, the lowest level, is 99 percent black, then level E, the highest, is only eight percent, in a country that is majoritively black, where whites are a minority and the equity act came in four years ago. [In Good Company: An Anatomy of Corporate Social Responsibility, Dinah Rajak, 2011]

  • Yes, but that presumably decides from a number of options put to it by various local authorities. In the end they do choose, majoritively-wise, a local authority project. [House of Commons, 1976]

  • Compare this majoritive state of the proud and conceited intellect of man, with the unproductive intellect of the technically-called insane, and say, if Shakspeare, in seeing through the mind; commonly called the ‘heart’ of man; . . . [Analysis of the Human Intellect, James Rush, 1865]

  • Majoritive mandates serve as the standard of value which is destined to achieve the twin objectives of political stability and the ‘utilitarian’ common good. [Global Mining Investing, Andrew Sheldon, 2014]

  • We must not allow ourselves or our programmers to misuse the power with which they have been entrusted by telling the public what it may or may not hear after that public has legitimately substantiated and voiced its majoritive approval. [Tarnished Gold: The Record Industry Revisted, R. Serge Denisoff, ‎1986]

  • Still, it is equally uncontestable that the image rendered by Ms. Guy is hardly a reflection of a whole and accurate, majoritive, image of male Afro-America. [Freedomways, 1979]

  • A “suspect class” has a history of purposeful unequal treatment and needs protection from the “majoritive political process.” [Proceedings of the NAPECW/NCPEAM National Conference, National College Physical Education Association for Men (U.S.), 1978]

  • In such a situation, society confronts a concretization quandary: there simply is no majoritatively acceptable way of reaching a majoritatively accepted goal. [Complexity: A Philosophical Overview, Nicholas Rescher, ‎1998]

  • However, the majoritatively entropic force driving protein folding cannot impart any degree of selectivity to binding. [Recognition Receptors in Biosensors, Mohammed Zourob, ‎2010]

  • Since as a practical matter juries may be majoritatively favorable to plaintiffs in drug and device products liability litigation, epidemiologic testimony may be impressive enough, in the absence of analytic guidelines from the judge, to sway them ... [Pharmacoepidemiology, Stanley Edlavitch, 1989]

  • Thirdly, that within a majoritative democracy, its government has a political mandate, if not a positive responsibilty, to prioritise this claim over any competing claims of its minorities. [The Twilight of Britain: Cultural Nationalism, Multiculturalism, and the Politics of Toleration, G. Gordon Betts, 2002]

  • One of the primary concerns regarding the exercise of judicial review is that it is counter-majoritative, allowing an unelected branch of government to determine the validity of the actions of the elected, political branches of government. [Strategies for Success in Law School and Beyond; Frank Read, Charles D. Cole, W. Scott Simpson; 2011]

So your instinct to derive this word using productive affixes is not original: other people have done the same thing, and a few of those even managed to find their way into print.

It is not a word that I myself would advise using; I think in almost all scenarios, a simpler wording is both possible and preferable. Much of the writing cited above is, I feel, a textbook example of how NOT to write — and just possibly, how NOT to derive new words without sounding risibly overbloviated.

But you really need to look at the in-print citations for yourself to see how these are being used by other people, and then decide for yourself whether you care for them or whether you might care to choose another way of expressing it. Constantly piling on derivational affixes to create new words can be ugly.

Again, check these citations and see for yourself:

  • majoritive
  • majoritively
  • majoritative
  • majoritatively

Solution 2:

Majority is overused, anyway. Best to restrict it to matters of voting.

Usually, the word most works just fine. Instead of majoritatively, use mostly.