How about sorting the array first? You then compare middle and first and last elements of the sorted array to find the dominant element.
public Integer findDominator(int[] arr) {
int[] arrCopy = arr.clone();
Arrays.sort(arrCopy);
int length = arrCopy.length;
int middleIndx = (length - 1) /2;
int middleIdxRight;
int middleIdxLeft = middleIndx;
if (length % 2 == 0) {
middleIdxRight = middleIndx+1;
} else {
middleIdxRight = middleIndx;
}
if (arrCopy[0] == arrCopy[middleIdxRight]) {
return arrCopy[0];
}
if (arrCopy[middleIdxLeft] == arrCopy[length -1]) {
return arrCopy[middleIdxLeft];
}
return null;
}