Eurovision Song Contest: collusion 2022 USING HYPER3

(takes five minute to run without cache; the time is spent in chunk dotest)

To cite the hyper2 package in publications, please use Hankin (2017). The file eurovision2022_jury_pre_null.txt, used below, refers to the jury vote for the 2022 Eurovision Song contest, pre-nullification; data supplied by Riley Uttley. First we specify the matrix as appearing in the Wikipedia page:

eurovision_table <- as.matrix(read.table("eurovision2022_jury_pre_null.txt", header = TRUE))
excluded <- c(2, 8, 12, 14,15,16)

contestants <- c(
"AU", # Australia        1
"AZ", # Azerbaijan       2 excluded
"BE", # Belgijm          3
"CY", # Cyprus           4
"CZ", # Czech republic   5
"EE", # Estonia          6
"FI", # Finland          7
"GE", # Georgia          8 excluded
"IE", # Ireland          9 
"IL", # Israel          10 
"MT", # Malta           11 
"ME", # Montenegro      12 excluded 
"MK", # North Macedonia 13
"PL", # Poland          14 excluded
"RO", # Romania         15 excluded
"SM", # San Marino      16 excluded
"RS", # Serbia          17
"SE"  # Sweden          18
)

(points <- sort(unique(c(eurovision_table)),decreasing=TRUE))

##  [1] 12 10  8  7  6  5  4  3  2  1  0

preference <- eurovision_table*0  
for(i in seq_along(points)){ preference[eurovision_table == points[i]] <- i }
preference

##    AU AZ BE CY CZ EE FI GE IE IL MT ME MK PL RO SM RS SE DE ES UK
## AU NA  7  3  2  3  2  2 10  6  2  2 11  6 10  6  7  9  1  5  2  8
## AZ  8 NA  8  5  7  5  4  1 11 11  7  3 10  2  4  5  3  6  2  1  3
## BE  3 11 NA  8  5  6 11 11  9  4 11 11  2 11 11 11  5  3  6  3  9
## CY 11 11 11 NA 11 11  8 11  7 11 11 10 11 11 11 11 11  9 11 11 11
## CZ  9 11  7  7 NA  4  5 11  2  5  4 11 11 11 11 11  7  5 11 11  2
## EE  6 11 11  4  4 NA  7  8  3  8  3 11  9  8  7 10  2  2  7 11  7
## FI 11  6  6  9  9  3 NA  9 11  6  8  9  7  6 11 11  6  7 10  9 11
## GE 10  2 11 11  6  8 11 NA 11 11 10  1 11  7  5  2 11 11  8 11 11
## IE  5 11 10 10 11  7 11  7 NA 11 11 11 11 11 10 11 11 11 11 11 11
## IL  2 11  4 11 11 11 11  6  8 NA  9 11 11 11 11  9 11  8  9  8 10
## MT 11 11 11 11 10 10 11 11  5  9 NA 11  5 11 11 11 11  4 11 11 11
## ME 11  4 11 11 11 11 11  2 11 11 11 NA  8  4  3  4  4 11 11 10 11
## MK  4 10 11 11  2 11  9 11 10 11  6  8 NA 11  8 11 10 11  1 11  4
## PL 11  1  5  3  8 11 10  5 11  3  5  6  3 NA  2  3  8 10 11  4  5
## RO 11  3 11 11 11  9 11  3 11  7 11  4 11  3 NA  1 11 11  3  7 11
## SM 11  5  1 11 11 11  6  4 11 11 11  5 11  1  1 NA 11 11 11 11 11
## RS  7  9  9  6 11 11  3 11  4 10 11  2  1  9  9  6 NA 11 11  6  6
## SE  1  8  2  1  1  1  1 11  1  1  1  7  4  5 11  8  1 NA  4  5  1

contestants[excluded]

## [1] "AZ" "GE" "ME" "PL" "RO" "SM"

H_excluded <- hyper3()
H_included <- hyper2()

text <- "remove this for R >= 4.6-0"
print(text)

## [1] "remove this for R >= 4.6-0"

`%notin%` <- Negate(`%in%`)

for(i in excluded){
    d <- preference[,i,drop=TRUE]
    d[d==11] <- 0
    newH <- suppfun(d[!is.na(d)])
    newH <- newH |> pwa23_multiple(contestants[excluded], "collusion")
    H_excluded <- H_excluded + newH
} # i loop closes

for(i in seq_len(ncol(preference))){
    if(i %notin% excluded){
        d <- preference[,i,drop=TRUE]
        d[d==11] <- 0
        d <- d[!is.na(d)]
        newH <- suppfun(d)
        H_included <- H_included + newH
    }
} # i loop closes

H_excluded

## log( (AU=1)^5 * (AU=1, AZ=1, BE=1, CY=1, CZ=1, EE=1, FI=1, GE=1, IE=1,
## IL=1, ME=1, MK=1, MT=1, PL=1, RO=1, RS=1, SE=1, collusion=5)^-1 *
## (AU=1, AZ=1, BE=1, CY=1, CZ=1, EE=1, FI=1, GE=1, IE=1, IL=1, ME=1,
## MK=1, MT=1, PL=1, RS=1, SE=1, SM=1, collusion=5)^-1 * (AU=1, AZ=1,
## BE=1, CY=1, CZ=1, EE=1, FI=1, GE=1, IE=1, IL=1, ME=1, MK=1, MT=1, PL=1,
## RS=1, SE=1, collusion=4)^-2 * (AU=1, AZ=1, BE=1, CY=1, CZ=1, EE=1,
## FI=1, GE=1, IE=1, IL=1, ME=1, MK=1, MT=1, RO=1, RS=1, SE=1, SM=1,
## collusion=5)^-1 * (AU=1, AZ=1, BE=1, CY=1, CZ=1, EE=1, FI=1, GE=1,
## IE=1, IL=1, ME=1, MK=1, MT=1, RO=1, RS=1, SE=1, collusion=4)^-1 *
## (AU=1, AZ=1, BE=1, CY=1, CZ=1, EE=1, FI=1, GE=1, IE=1, IL=1, ME=1,
## MK=1, MT=1, RS=1, SE=1, collusion=3)^-1 * (AU=1, AZ=1, BE=1, CY=1,
## CZ=1, EE=1, FI=1, GE=1, IE=1, IL=1, MK=1, MT=1, PL=1, RO=1, RS=1, SE=1,
## SM=1, collusion=5)^-1 * (AU=1, AZ=1, BE=1, CY=1, CZ=1, EE=1, FI=1,
## GE=1, IE=1, IL=1, MK=1, MT=1, RS=1, SE=1, collusion=2)^-1 * (AU=1,
## AZ=1, BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1, ME=1, MK=1, MT=1, PL=1,
## RO=1, RS=1, SE=1, SM=1, collusion=5)^-1 * (AU=1, AZ=1, BE=1, CY=1,
## CZ=1, EE=1, FI=1, IE=1, IL=1, ME=1, MK=1, MT=1, PL=1, RS=1, SE=1,
## collusion=3)^-1 * (AU=1, AZ=1, BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1,
## IL=1, ME=1, MK=1, MT=1, RS=1, SE=1, collusion=2)^-1 * (AU=1, AZ=1,
## BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1, MK=1, MT=1, PL=1, RO=1, RS=1,
## SE=1, SM=1, collusion=4)^-1 * (AU=1, AZ=1, BE=1, CY=1, CZ=1, EE=1,
## FI=1, IE=1, IL=1, MK=1, MT=1, PL=1, RO=1, SE=1, SM=1, collusion=4)^-1 *
## (AU=1, AZ=1, BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1, MK=1, MT=1,
## RS=1, SE=1, collusion=1)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1,
## GE=1, IE=1, IL=1, ME=1, MK=1, MT=1, PL=1, RO=1, RS=1, SE=1, SM=1,
## collusion=5)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, GE=1, IE=1,
## IL=1, ME=1, MK=1, MT=1, RO=1, RS=1, SE=1, SM=1, collusion=4)^-1 *
## (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, GE=1, IE=1, IL=1, ME=1, MK=1,
## MT=1, RO=1, RS=1, SE=1, collusion=3)^-1 * (AU=1, BE=1, CY=1, CZ=1,
## EE=1, FI=1, GE=1, IE=1, IL=1, ME=1, MK=1, MT=1, RS=1, SE=1,
## collusion=2)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, GE=1, IE=1,
## IL=1, MK=1, MT=1, RS=1, SE=1, collusion=1)^-2 * (AU=1, BE=1, CY=1,
## CZ=1, EE=1, FI=1, GE=1, IE=1, IL=1, MK=1, MT=1, RS=1, collusion=1)^-1 *
## (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1, ME=1, MK=1, MT=1,
## PL=1, RO=1, RS=1, SE=1, SM=1, collusion=4)^-1 * (AU=1, BE=1, CY=1,
## CZ=1, EE=1, FI=1, IE=1, IL=1, ME=1, MK=1, MT=1, RO=1, RS=1, SE=1, SM=1,
## collusion=3)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1,
## ME=1, MK=1, MT=1, RS=1, SE=1, SM=1, collusion=2)^-1 * (AU=1, BE=1,
## CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1, MK=1, MT=1)^-1 * (AU=1, BE=1, CY=1,
## CZ=1, EE=1, FI=1, IE=1, IL=1, MK=1, MT=1, PL=1, RO=1, RS=1, SE=1, SM=1,
## collusion=3)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1,
## MK=1, MT=1, PL=1, RO=1, SE=1, SM=1, collusion=3)^-1 * (AU=1, BE=1,
## CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1, MK=1, MT=1, PL=1, RS=1, SE=1, SM=1,
## collusion=2)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1,
## MK=1, MT=1, PL=1, RS=1, SE=1, collusion=1)^-1 * (AU=1, BE=1, CY=1,
## CZ=1, EE=1, FI=1, IE=1, IL=1, MK=1, MT=1, PL=1, SE=1, SM=1,
## collusion=2)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1,
## MK=1, MT=1, PL=1, SE=1, collusion=1)^-1 * (AU=1, BE=1, CY=1, CZ=1,
## EE=1, FI=1, IE=1, IL=1, MK=1, MT=1, RS=1, SE=1)^-4 * (AU=1, BE=1, CY=1,
## CZ=1, EE=1, FI=1, IE=1, IL=1, MK=1, MT=1, RS=1, SE=1, SM=1,
## collusion=1)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1,
## MK=1, MT=1, SE=1)^-2 * (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1,
## MT=1)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1, MK=1, MT=1, RS=1,
## SE=1)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, MK=1, MT=1, RS=1,
## SE=1)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, GE=1, IE=1, IL=1, MK=1, MT=1,
## RS=1, collusion=1)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, IE=1, IL=1,
## MK=1, MT=1, RS=1)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, IE=1, IL=1, MK=1,
## MT=1, RS=1, SE=1)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, IE=1, IL=1,
## MT=1)^-1 * (AU=1, BE=1, CY=1, CZ=1, FI=1, MK=1, MT=1, RS=1, SE=1)^-1 *
## (AU=1, BE=1, CY=1, CZ=1, IE=1, IL=1, MK=1, MT=1)^-1 * (AU=1, BE=1,
## CY=1, CZ=1, IE=1, IL=1, MK=1, MT=1, RS=1)^-1 * (AU=1, BE=1, CY=1, CZ=1,
## MK=1, MT=1, RS=1, SE=1)^-1 * (AZ=1, collusion=1)^5 * (BE=1, CY=1, CZ=1,
## EE=1, FI=1, IE=1, IL=1, MK=1, MT=1)^-1 * (BE=1, CY=1, CZ=1, EE=1, FI=1,
## IE=1, IL=1, MK=1, MT=1, RS=1, SE=1)^-1 * (BE=1, CY=1, CZ=1, EE=1, FI=1,
## IE=1, IL=1, MK=1, MT=1, SE=1)^-1 * (BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1,
## MK=1, MT=1)^-1 * (BE=1, CY=1, CZ=1, EE=1, IE=1, IL=1, MK=1, MT=1)^-1 *
## (BE=1, CY=1, CZ=1, EE=1, IE=1, IL=1, MK=1, MT=1, RS=1)^-1 * (BE=1,
## CY=1, CZ=1, EE=1, IE=1, IL=1, MK=1, MT=1, RS=1, SE=1)^-1 * (BE=1, CY=1,
## CZ=1, FI=1, IE=1, IL=1, MK=1, MT=1, RS=1, SE=1)^-1 * (BE=1, CY=1, CZ=1,
## FI=1, IE=1, IL=1, MT=1, RS=1, SE=1)^-1 * (BE=1, CY=1, CZ=1, FI=1, IE=1,
## IL=1, MT=1, SE=1)^-1 * (CY=1)^1 * (EE=1)^4 * (FI=1)^4 * (GE=1,
## collusion=1)^5 * (IE=1)^2 * (IL=1)^2 * (ME=1, collusion=1)^5 * (MK=1)^3
## * (PL=1, collusion=1)^5 * (RO=1, collusion=1)^5 * (RS=1)^5 * (SE=1)^4 *
## (SM=1, collusion=1)^5)

mHex <- maxp(H_excluded)
mHin <- maxp(H_included)

dotchart(mHex)

dotchart(mHin)

H <- H_excluded + as.hyper3(H_included)

result <- specificp.gt.test(H, "collusion",0)

result

## 
##  Constrained support maximization
## 
## data:  H
## null hypothesis: sum p_i=1, collusion <= 0 (notional)
## null estimate:
##         AU         AZ         BE  collusion         CY         CZ         EE 
## 6.1282e-02 5.9831e-02 5.7187e-02 9.9992e-06 4.0474e-02 5.7588e-02 5.9735e-02 
##         FI         GE         IE         IL         ME         MK         MT 
## 5.9759e-02 6.0477e-02 4.7404e-02 5.1527e-02 5.4253e-02 5.2925e-02 4.7784e-02 
##         PL         RO         RS         SE         SM 
## 6.0014e-02 5.4676e-02 5.9889e-02 6.2235e-02 5.2952e-02 
## (argmax, constrained optimization)
## Support for null:  -516.43 + K
## 
## alternative hypothesis:  sum p_i=1 
## alternative estimate:
##        AU        AZ        BE collusion        CY        CZ        EE        FI 
## 0.0344036 0.0135341 0.0102911 0.7894534 0.0019374 0.0093836 0.0157357 0.0104451 
##        GE        IE        IL        ME        MK        MT        PL        RO 
## 0.0026084 0.0029277 0.0056896 0.0015347 0.0067886 0.0031701 0.0088627 0.0021538 
##        RS        SE        SM 
## 0.0099053 0.0701155 0.0010597 
## (argmax, free optimization)
## Support for alternative:  -414.79 + K
## 
## degrees of freedom: 1
## support difference = 101.63
## p-value: 4.0407e-46 (one-sided)

H_excluded

## log( (AU=1)^5 * (AU=1, AZ=1, BE=1, CY=1, CZ=1, EE=1, FI=1, GE=1, IE=1,
## IL=1, ME=1, MK=1, MT=1, PL=1, RO=1, RS=1, SE=1, collusion=5)^-1 *
## (AU=1, AZ=1, BE=1, CY=1, CZ=1, EE=1, FI=1, GE=1, IE=1, IL=1, ME=1,
## MK=1, MT=1, PL=1, RS=1, SE=1, SM=1, collusion=5)^-1 * (AU=1, AZ=1,
## BE=1, CY=1, CZ=1, EE=1, FI=1, GE=1, IE=1, IL=1, ME=1, MK=1, MT=1, PL=1,
## RS=1, SE=1, collusion=4)^-2 * (AU=1, AZ=1, BE=1, CY=1, CZ=1, EE=1,
## FI=1, GE=1, IE=1, IL=1, ME=1, MK=1, MT=1, RO=1, RS=1, SE=1, SM=1,
## collusion=5)^-1 * (AU=1, AZ=1, BE=1, CY=1, CZ=1, EE=1, FI=1, GE=1,
## IE=1, IL=1, ME=1, MK=1, MT=1, RO=1, RS=1, SE=1, collusion=4)^-1 *
## (AU=1, AZ=1, BE=1, CY=1, CZ=1, EE=1, FI=1, GE=1, IE=1, IL=1, ME=1,
## MK=1, MT=1, RS=1, SE=1, collusion=3)^-1 * (AU=1, AZ=1, BE=1, CY=1,
## CZ=1, EE=1, FI=1, GE=1, IE=1, IL=1, MK=1, MT=1, PL=1, RO=1, RS=1, SE=1,
## SM=1, collusion=5)^-1 * (AU=1, AZ=1, BE=1, CY=1, CZ=1, EE=1, FI=1,
## GE=1, IE=1, IL=1, MK=1, MT=1, RS=1, SE=1, collusion=2)^-1 * (AU=1,
## AZ=1, BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1, ME=1, MK=1, MT=1, PL=1,
## RO=1, RS=1, SE=1, SM=1, collusion=5)^-1 * (AU=1, AZ=1, BE=1, CY=1,
## CZ=1, EE=1, FI=1, IE=1, IL=1, ME=1, MK=1, MT=1, PL=1, RS=1, SE=1,
## collusion=3)^-1 * (AU=1, AZ=1, BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1,
## IL=1, ME=1, MK=1, MT=1, RS=1, SE=1, collusion=2)^-1 * (AU=1, AZ=1,
## BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1, MK=1, MT=1, PL=1, RO=1, RS=1,
## SE=1, SM=1, collusion=4)^-1 * (AU=1, AZ=1, BE=1, CY=1, CZ=1, EE=1,
## FI=1, IE=1, IL=1, MK=1, MT=1, PL=1, RO=1, SE=1, SM=1, collusion=4)^-1 *
## (AU=1, AZ=1, BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1, MK=1, MT=1,
## RS=1, SE=1, collusion=1)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1,
## GE=1, IE=1, IL=1, ME=1, MK=1, MT=1, PL=1, RO=1, RS=1, SE=1, SM=1,
## collusion=5)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, GE=1, IE=1,
## IL=1, ME=1, MK=1, MT=1, RO=1, RS=1, SE=1, SM=1, collusion=4)^-1 *
## (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, GE=1, IE=1, IL=1, ME=1, MK=1,
## MT=1, RO=1, RS=1, SE=1, collusion=3)^-1 * (AU=1, BE=1, CY=1, CZ=1,
## EE=1, FI=1, GE=1, IE=1, IL=1, ME=1, MK=1, MT=1, RS=1, SE=1,
## collusion=2)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, GE=1, IE=1,
## IL=1, MK=1, MT=1, RS=1, SE=1, collusion=1)^-2 * (AU=1, BE=1, CY=1,
## CZ=1, EE=1, FI=1, GE=1, IE=1, IL=1, MK=1, MT=1, RS=1, collusion=1)^-1 *
## (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1, ME=1, MK=1, MT=1,
## PL=1, RO=1, RS=1, SE=1, SM=1, collusion=4)^-1 * (AU=1, BE=1, CY=1,
## CZ=1, EE=1, FI=1, IE=1, IL=1, ME=1, MK=1, MT=1, RO=1, RS=1, SE=1, SM=1,
## collusion=3)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1,
## ME=1, MK=1, MT=1, RS=1, SE=1, SM=1, collusion=2)^-1 * (AU=1, BE=1,
## CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1, MK=1, MT=1)^-1 * (AU=1, BE=1, CY=1,
## CZ=1, EE=1, FI=1, IE=1, IL=1, MK=1, MT=1, PL=1, RO=1, RS=1, SE=1, SM=1,
## collusion=3)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1,
## MK=1, MT=1, PL=1, RO=1, SE=1, SM=1, collusion=3)^-1 * (AU=1, BE=1,
## CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1, MK=1, MT=1, PL=1, RS=1, SE=1, SM=1,
## collusion=2)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1,
## MK=1, MT=1, PL=1, RS=1, SE=1, collusion=1)^-1 * (AU=1, BE=1, CY=1,
## CZ=1, EE=1, FI=1, IE=1, IL=1, MK=1, MT=1, PL=1, SE=1, SM=1,
## collusion=2)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1,
## MK=1, MT=1, PL=1, SE=1, collusion=1)^-1 * (AU=1, BE=1, CY=1, CZ=1,
## EE=1, FI=1, IE=1, IL=1, MK=1, MT=1, RS=1, SE=1)^-4 * (AU=1, BE=1, CY=1,
## CZ=1, EE=1, FI=1, IE=1, IL=1, MK=1, MT=1, RS=1, SE=1, SM=1,
## collusion=1)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1,
## MK=1, MT=1, SE=1)^-2 * (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1, IL=1,
## MT=1)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1, MK=1, MT=1, RS=1,
## SE=1)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, FI=1, MK=1, MT=1, RS=1,
## SE=1)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, GE=1, IE=1, IL=1, MK=1, MT=1,
## RS=1, collusion=1)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, IE=1, IL=1,
## MK=1, MT=1, RS=1)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, IE=1, IL=1, MK=1,
## MT=1, RS=1, SE=1)^-1 * (AU=1, BE=1, CY=1, CZ=1, EE=1, IE=1, IL=1,
## MT=1)^-1 * (AU=1, BE=1, CY=1, CZ=1, FI=1, MK=1, MT=1, RS=1, SE=1)^-1 *
## (AU=1, BE=1, CY=1, CZ=1, IE=1, IL=1, MK=1, MT=1)^-1 * (AU=1, BE=1,
## CY=1, CZ=1, IE=1, IL=1, MK=1, MT=1, RS=1)^-1 * (AU=1, BE=1, CY=1, CZ=1,
## MK=1, MT=1, RS=1, SE=1)^-1 * (AZ=1, collusion=1)^5 * (BE=1, CY=1, CZ=1,
## EE=1, FI=1, IE=1, IL=1, MK=1, MT=1)^-1 * (BE=1, CY=1, CZ=1, EE=1, FI=1,
## IE=1, IL=1, MK=1, MT=1, RS=1, SE=1)^-1 * (BE=1, CY=1, CZ=1, EE=1, FI=1,
## IE=1, IL=1, MK=1, MT=1, SE=1)^-1 * (BE=1, CY=1, CZ=1, EE=1, FI=1, IE=1,
## MK=1, MT=1)^-1 * (BE=1, CY=1, CZ=1, EE=1, IE=1, IL=1, MK=1, MT=1)^-1 *
## (BE=1, CY=1, CZ=1, EE=1, IE=1, IL=1, MK=1, MT=1, RS=1)^-1 * (BE=1,
## CY=1, CZ=1, EE=1, IE=1, IL=1, MK=1, MT=1, RS=1, SE=1)^-1 * (BE=1, CY=1,
## CZ=1, FI=1, IE=1, IL=1, MK=1, MT=1, RS=1, SE=1)^-1 * (BE=1, CY=1, CZ=1,
## FI=1, IE=1, IL=1, MT=1, RS=1, SE=1)^-1 * (BE=1, CY=1, CZ=1, FI=1, IE=1,
## IL=1, MT=1, SE=1)^-1 * (CY=1)^1 * (EE=1)^4 * (FI=1)^4 * (GE=1,
## collusion=1)^5 * (IE=1)^2 * (IL=1)^2 * (ME=1, collusion=1)^5 * (MK=1)^3
## * (PL=1, collusion=1)^5 * (RO=1, collusion=1)^5 * (RS=1)^5 * (SE=1)^4 *
## (SM=1, collusion=1)^5)

summary(H_excluded)

## A hyper3 object of size 19.
## pnames:  AU AZ BE collusion CY CZ EE FI GE IE IL ME MK MT PL RO RS SE SM 
## Number of brackets: 69 
## Sum of powers: 0 
## 
## Table of bracket lengths:
##  1  2  8  9 10 11 12 13 14 15 16 17 18 
##  9  6  6  6  6  4  2  2  5  6  6  5  6 
## 
## Table of powers:
## -4 -2 -1  1  2  3  4  5 
##  1  3 50  1  2  1  3  8 
## 
## Table of weights:
##   1   2   3   4   5 
## 702   6   6   6   6

summary(H)

## A hyper3 object of size 19.
## pnames:  AU AZ BE collusion CY CZ EE FI GE IE IL ME MK MT PL RO RS SE SM 
## Number of brackets: 220 
## Sum of powers: 0 
## 
## Table of bracket lengths:
##  1  2  8  9 10 11 12 13 14 15 16 17 18 
## 18  6 18 21 21 19 17 17 20 19 19 18  7 
## 
## Table of powers:
##  -4  -3  -2  -1   2   3   4   5   6  10  11  12  13  14  15  16  18  19 
##   1   1   9 185   1   1   2   7   2   1   3   1   1   1   1   1   1   1 
## 
## Table of weights:
##    1    2    3    4    5 
## 2484    6    6    6    6

Hankin, R. K. S. 2017. “Partial Rank Data with the hyper2 Package: Likelihood Functions for Generalized Bradley-Terry Models.” The R Journal 9 (2): 429–39.

Eurovision Song Contest: collusion 2022 USING HYPER3

R. K. S. Hankin