
431 A.2d 1206 (1981)
Dennis J. ROBERTS II, Attorney General et al.
v.
COMMUNICATIONS INVESTMENT CLUB OF WOONSOCKET et al.
No. 79-294-Appeal.
Supreme Court of Rhode Island.
July 1, 1981.
*1207 Dennis J. Roberts, II, Atty. Gen., Joshua Teverow, Sp. Asst. Atty. Gen., for plaintiffs.
Stone, Clifton & Clifton, Walter R. Stone, Providence, for defendants.

OPINION
MURRAY, Justice.
On May 7, 1979, the Attorney General filed a complaint in the Superior Court charging the defendants with operating an unauthorized lottery in violation of Art. XLI, sec. 1 of the Rhode Island Constitution. The complaint sought to enjoin the defendants' activities permanently and after a hearing of the Attorney General's allegations, such relief was granted by a Superior Court justice. It is the granting of the requested relief which forms the basis of the defendants' appeal.
On May 1, 1979, articles of association were filed in the Secretary of State's office *1208 by the individually named defendants[1] to incorporate the Communications Investment Club of Woonsocket, a nonbusiness corporation. The articles of incorporation stated that the corporate purpose was to bring "people together within and without the state of Rhode Island for the purpose of fostering communications, understanding and trust for our fellow human beings."
The record discloses that the Communications Investment Club operated in the following manner. Each person who wished to participate in its plan was required to invest $1,000. Such an investment entitled the investor to the privilege of having his name placed on a list containing names of six other investors. The $1,000 investment was divided equally between the person whose name appeared first on the list and the person whose name appeared last on the list. After the person whose name appeared first on the list had received all of the money he was to receive according to the plan, his name was stricken from the list. Once this was done, the remaining names on the list were all advanced one position and the name of the newest investor was inserted into the sixth position at the bottom of the list. Once an investor's name cleared the first list, he was entitled to invest in another list, which operated in a similar manner.
On appeal, two issues have been raised for our consideration. One of the individual defendants named in the complaint, Vincent A. Scirocco (Scirocco), contends that he was deprived of his Fifth Amendment privilege against self-incrimination when the trial justice directed him to answer certain questions after he had refused to answer on the grounds that the answers might have incriminated him. The other issue raised is wither defendants' activities constituted a "lottery" within the meaning of R.I. Const. Art. XLI, sec. 1.

I
With respect to the first issue, defendant Scirocco contends that the trial justice erred in directing him to answer certain questions after he had invoked his Fifth Amendment privilege against self-incrimination. The Attorney General, on the other hand, contends that the answers to the questions given by defendant Scirocco could not have incriminated him and that, at any rate, defendant had waived his right to assert his Fifth Amendment privilege.
At this juncture, it would be well to examine the law material to the issues raised by the parties. The constitutional privilege against self-incrimination accords one the right to refuse to incriminate himself. Such privilege extends not only to disclosures that would support a conviction but also to disclosures that would constitute a link in a chain of evidence needed to initiate a prosecution. Hummell v. Superior Court, 100 R.I. 54, 58-59, 211 A.2d 272, 274 (1965) (citing Malloy v. Hogan, 378 U.S. 1, 11, 84 S.Ct. 1489, 1495, 12 L.Ed.2d 653, 661 (1964)).[2] Although a witness is not exonerated from answering questions by merely declaring that in so doing he would incriminate himself, it must be "`perfectly clear, from a careful consideration of all the circumstances in the case, that the witness is mistaken, and that the answer cannot possibly have such tendency' to incriminate." Hoffman v. United States, 341 U.S. 479, 488, 71 S.Ct. 814, 819, 95 L.Ed. 1118, 1125 (1951) (Emphasis in original.)
Accordingly, a waiver of such a privilege is not lightly to be inferred. Smith v. United States, 337 U.S. 137, 150, 69 S.Ct. 1000, 1007, 93 L.Ed. 1264, 1274 (1949). Indeed "`courts indulge in every reasonable presumption against waiver' of fundamental constitutional rights * * *." (Footnote omitted.) Johnson v. Zerbst, 304 U.S. 458, 464, 58 S.Ct. 1019, 1023, 82 L.Ed. 1461, 1466 (1938). To waive this or any *1209 other fundamental constitutional right, one must intentionally relinquish or abandon a known right or privilege; and whether particular conduct amounts to a waiver must be determined from the circumstances of each case. Id. at 464, 58 S.Ct. at 1023, 82 L.Ed. at 1466; Hummell v. Superior Court, 100 R.I. at 58, 211 A.2d at 274 (citing Johnson v. Zerbst, supra).
With the foregoing analysis as our guide, we now examine the following colloquy that took place during Scirocco's testimony.[3]
"MR. STONE: Your Honor, before Mr. Teverow begins I'd like to place on the record that I've advised Mr. Scirocco he does not have to testify, that 11-19-1 of the General Laws carries with it punishment up to two years in jail and a $2,000 fine. It's a criminal sanction and that under the Fifth Amendment he has a right to remain silent.
"Q Mr. Scirocco are you familiar with an operation or project known as Platinum Pyramid or Circle of Platinum scheme?
"A Your Honor, have I been granted immunity?
"THE COURT: I'm not aware of any immunity being granted. I can't answer your question Mr. Scirocco. You'll have to either speak to counsel or counsel will have to confer with the Attorney General.
"MR. STONE: To the best of my knowledge, he hasn't been granted any immunity.
"MR. TEVEROW: Defendant hasn't been granted any criminal immunity.
"A I refused [sic].
"* * *
"THE COURT: Have you heard the question?
"THE WITNESS: Yes[.]
"THE COURT: All right. I don't see that it incriminates him in any manner. You may answer.
"* * *
"THE COURT: I would assume both you and Mr. Teverow are familiar with that kind of a scheme and I don't think it incriminates you in any criminal responsibility.
"MR. STONE: But I've advised my client to take the Fifth on all the questions. Now is he going to get partial immunity? I would think there has to be some consistency here.
"THE COURT: We'll take it question by question. You may answer.
"A Yes I am.
"Q Have you ever participated in or promoted or organized such a scheme?
"MR. STONE: Your Honor, I'd advise my client to take the Fifth Amendment.
"A And I do[.]
"THE COURT: Well, we have to see if he wishes to take the Fifth Amendment.
"THE WITNESS: I do wish to take the Fifth Amendment to that question.
"THE COURT: All right, I would require you to answer Mr. Scirocco. Would you answer please.
"* * *
"A First of all, I don't refer to it as a scheme, which you do. All it is is an investment, you put up a certain amount of money and you give it to two different people in hopes that eventually as your name proceeds through a list, you would receive something for your original investment."
Later during Scirocco's testimony the following occurred:
"Q Could you please explain to the Court, Mr. Scirocco, to the best of your knowledge, how the Circle of Platinum worked?
"* * *
"A I've got to repeat [sic] all over again?
"* * *
"THE COURT: The very first response that this witness gave was he was familiar *1210 with the operation of this plan. Now we're seeking to determine what the extent of his knowledge is. Tell us what you know about it.
"A It's investments that you put up a certain amount of money and you give it to two different people and as your name is entered onto a list, and proceeds to the top of the list, when you get to the top of the list, then you receive from other members. It's gifts. I give to you and eventually you're going to give to me. As simple as that. I think it's very simple and basic."
The Attorney General then introduced into evidence a verified complaint that defendant Scirocco and the others had previously filed in another related case that they had initiated in the United States District Court for the District of Rhode Island.[4]
This document was introduced into evidence as a full exhibit without objection by defendants. The complaint reads, in pertinent part:
"`the Circle of Platinum,' * * * involves individuals investing $1,000 for the right to have their name placed on two lists with other individuals, the lists comprising [sic] of six names. The individual investors gave the no. six name $500 and the no. one name $500. The no. one name is then taken off the list, and the remaining five names move up, allowing the new investor to become no. six. The first person who invests after them gives them $500, which allows them to recoup 50 percent of their investment. Assuming five more individuals invest, they recoup the entire $1,000. After they have cleared the first list, going six through 1, and recoup their investment, individuals then may buy into their second list from which they would realize a profit.
"* * *
"Plaintiff Vincent A. Scirocco, as individual plaintiff, has been an investor in the `Circle of Platinum.'"
Assuming, without deciding, that the answers that Scirocco was compelled to give were incriminating under the above-cited cases and that the trial justice therefore erred in requesting Scirocco to give those answers, we conclude that such error, if indeed it was error, was harmless. Even if the trial justice had upheld Scirocco's assertion of his privilege against self-incrimination and had not requested Scirocco to answer the questions posed to him, the same information the questions sought to elicit was eventually placed before the trial justice when plaintiffs introduced into evidence without objection by defendants the federal court complaint.
The circumstances of this case are not unlike those in Major v. Grieg, 102 R.I. 379, 230 A.2d 846 (1967). In that case, the plaintiff objected to the admission into evidence of a police report which disclosed that she had admitted fault in an automobile accident in which she was involved with the defendant; however, earlier in the trial the police officer had, without any objection by the plaintiff, read into evidence his version of the statement that the plaintiff had given to him after the accident. According to the police officer, the plaintiff had said the accident was no fault of the defendant. We held that the admission of the report was not prejudicial error, if it was error at all. Id. at 393, 230 A.2d at 854.
Furthermore, we cannot say that the testimony in controversy here so influenced the judgment of the trial justice as to have caused him to rest his decision in whole or in substantial part on that evidence. See Corrado v. Providence Redevelopment Agency, 110 R.I. 549, 556-57, 294 A.2d 387, 390 (1972). Indeed the trial justice need not have taken any of the disputed evidence into account in arriving at his decision. Thus, we hold that under the circumstances of this case, if it was error for the trial justice to compel defendant to answer questions posed to him after he had asserted his privilege against self-incrimination, such error was harmless.


*1211 II
Turning now to defendants' contention that their activities did not constitute a lottery and are not, therefore, proscribed by our constitution, we find the applicable provision embodied in Art. XLI, sec. 1 of the Rhode Island Constitution, which provides:
"All lotteries shall hereafter be prohibited in the state except lotteries operated by the state and except those previously permitted by the general assembly prior to adoption of this amendment, and all shall hereafter be subject to the prescription and regulation of the general assembly; provided that before the adoption of this amendment no other lotteries shall be permitted or authorized."
It is well settled that a "lottery" proscribed in either a state constitution or statute is defined as a scheme or a plan having three essential elements: consideration, chance, and prize. Goodwill Advertising Co. v. Elmwood Amusement Corp., 86 R.I. 6, 12, 133 A.2d 644, 647 (1957). All three elements must be present before a scheme may be termed a lottery. If one of them is absent, the scheme is not a lottery, regardless of its purpose. If all of the elements are present, the scheme is a lottery, regardless of the purpose of its sponsor. Morrow v. State, 511 P.2d 127, 128 (Alaska 1973); accord, Cudd v. Aschenbrenner, 233 Or. 272, 377 P.2d 150 (1962); State v. Wassick, 156 W. Va. 12, 191 S.E.2d 283 (1972).
In the case at bar, there is little dispute that the elements of consideration and prize are present. The consideration is the $1,000 that each investor invests in the hope of receiving $32,000, which is the prize. What is disputed by the parties, however, is whether the element of chance is present.
In deciding whether the element of chance is present, we adopt, as have most jurisdictions which have faced this issue, the "dominant factor" doctrine, under which a scheme constitutes a lottery when an element of chance dominates the distribution of prizes, even though such a distribution is affected to some degree by the exercise of skill or judgment.[5]
Although the scheme in the instant case may have involved some degree of skill or judgment, it is clear that the element of chance permeated it. The operation in the instant case has all the attributes of what is commonly referred to as a "pyramid" scheme. The Attorney General in his brief to this court made the following observations:
"As soon as the two lists with the investor placed in sixth position are `sold,' the investor receives $500.00 from each `sale' for a total of $1,000.00. Then, by the time the investor's name reaches the top spot on the list, he will occupy that spot on sixty four lists because of the constant duplication. The investor will then receive $500.00 from each of the `purchasers' of those sixty four lists, for a total of $32,000.00. This profit, combined with the $1,000.00 received earlier from being in the sixth position on two lists, gives the investor a total return of $33,000.00.
"In other words, the geometric progression of the `Platinum' scheme creates a pyramid with the person who is number one on the list at the apex of the pyramid, and the person who is number six on the list at the base of the pyramid or the sixth level. In order for the sixth person to rise to the apex (or number one position) of the pyramid, a number of unbroken geometrically progressive chain sales are required; i.e., in order for the sixth person to receive the promised $32,000.00 profit he needs to obtain $500.00 from each of sixty four new members entering the pyramid at the base or sixth level, *1212 which means there must have been an unbroken geometric chain of membership and payment of $1,000.00 keeping the scheme alive through all the intermediate levels of two through six.
"For example, if as reported in the local media during the week of April 30, 1979, five hundred persons were participating in the `Platinum Pyramid,' it would take thirty two thousand new recruits to enable each of those five hundred persons to reach the top of sixty four lists and thus receive the $32,000.00 profit. But, to enable those thirty two thousand new recruits to each reach the top of sixty four lists and thus receive the $32,000.00 profit, it would take two million forty eight thousand (2,048,000) people. The addition of new memberships and the continuation of the geometric progression would quickly use up the entire population of Rhode Island, then the population of the United States, and then the world, should the chain work perfectly."
Other state courts have found that similar schemes constitute illegal lotteries. In Sherwood & Roberts-Yakima, Inc. v. Leach, 67 Wash.2d 630, 635, 409 P.2d 160, 163 (1965), the Supreme Court of Washington, in discussing the element of chance involved in a scheme whose success was also dependent upon its members inducing other persons to invest, stated:
"Assuming that respondents in fact used skill or judgment in selecting the referrals, the trial court properly held that chance permeates the entire scheme. The court found that respondents took a chance that the referrals might not be interested; that the salesman might not adequately make his presentation; that the referral might have already been referred by someone else; that the market might be saturated; and that the salesman might not even contact the referral."
Yet another commentator has stated:
"Pyramid schemes possess the three essential elements of a lottery. The substantial sums participants invest in the schemes constitute the necessary consideration and the receipt by the participants of profits resulting from the recruiting of others satisfies the prize element. The element of chance is present because the financial gain of any participant is the result of factors outside his control: the action of prior participants, the degree of market saturation, and the prospects of an individual continuing the recruiting chain." (Footnotes omitted.) Pyramid Schemes: Dare to Be Regulated, 61 Geo.L.J. 1257, 1269 (1973).
In addition, there is a substantial body of case law which supports this view. E. g., State v. Bull Investment Group, Inc., 32 Conn. Supp. 279, 351 A.2d 879 (1974); Commonwealth v. Allen, 404 S.W.2d 464 (Ky. 1966); Sherwood & Roberts-Yakima, Inc. v. Leach, supra.
In view of the evidence and the authorities cited, we conclude that the dominant factors in the success or failure of this scheme were beyond the control of the participants.[6] Thus, chance is a dominant element of this scheme and therefore we deem it to be a violation of R.I.Const. Art. XLI, sec. 1.
Accordingly, the defendants' appeal is denied and dismissed, the judgment appealed from is affirmed, and the case is remanded to the Superior Court.
NOTES
[1]  The individually named defendants who filed the articles of association were Vincent A. Scirocco, Evelina Masse, Hank Daigle, Pauline Baurden, and Paul Pickett.
[2]  In Malloy v. Hogan, 378 U.S. 1, 84 S.Ct. 1489, 12 L.Ed.2d 653 (1964), the Malloy court relied upon Hoffman v. United States, 341 U.S. 479, 71 S.Ct. 814, 95 L.Ed. 1118 (1951), as precedent.
[3]  Scirocco was called as a witness by the Attorney General under our adverse-witness statute, G.L. 1956 (1969 Reenactment) § 9-17-14.
[4]  In the federal court case, defendants sought injunctive relief against the Attorney General and others to enjoin them from interfering with their operation.
[5]  E. g., Morrow v. State, 511 P.2d 127 (Alaska 1973); Finster v. Keller, 18 Cal. App.3d 836, 96 Cal. Rptr. 241 (1971); State v. Steever, 103 N.J. Super. 149, 246 A.2d 743 (1968); Commonwealth v. Laniewski, 173 Pa.Super. 245, 98 A.2d 215 (1953); Seattle Times Co. v. Tielsch, 80 Wash.2d 502, 495 P.2d 1366 (1972). This doctrine is opposed to the "pure chance" doctrine, under which a scheme is considered a lottery when a person's judgment plays no part in the selection and award of the prize. See Braddock v. Family Finance Corp., 95 Idaho 256, 506 P.2d 824 (1973).
[6]  Among these factors are market saturation and the likely prospect that not enough new investors will be found in order to ensure a profit to all investors.
