What does $w_{ni}$ mean in the weighted nearest neighbour classifier? Wiki gives this definition of KNN

In pattern recognition, the k-nearest neighbors algorithm (k-NN) is a
  non-parametric method used for classification and regression. In both
  cases, the input consists of the k closest training examples in the
  feature space. The output depends on whether k-NN is used for
  classification or regression:
  
  
*
  
*In k-NN classification, the output is a class membership. An object    is classified by a plurality vote of its neighbors, with the object
  being assigned to the class most common among its k nearest neighbors 
  (k is a positive integer, typically small). If k = 1, then the object 
  is simply assigned to the class of that single nearest neighbor.
  
*In k-NN regression, the output is the property value for the object.    This value is the average of the values of k nearest
  neighbors.
  

and this explanation about "The weighted nearest neighbour classifier"

The k-nearest neighbour classifier can be viewed as assigning the k
  nearest neighbours a weight 1/k and all others 0 weight. This can be
  generalised to weighted nearest neighbour classifiers. That is, where
  the ith nearest neighbour is assigned a weight ${\displaystyle
> w_{ni}}$, with ${\displaystyle \sum _{i=1}^{n}w_{ni}=1}$. An analogous
  result on the strong consistency of weighted nearest neighbour
  classifiers also holds.

this $w_{ni}$ confuses me a lot.
taking the iris dataset as the example, there are 150 data points, if we choose k=50, are there top 50 neighbours, each of which has a 1/50 weight, and the other 100 data points 0 weight.
if it is, $w_i = 1/50$ where $i=1, 2, ..., 50$.
so, what does $w_{ni}$ mean?
Assume $_{1}$ represents the nearest neighbor, $_{2}$ represents the second nearest neighbor, what does "n" in $_{i}$=1/50 mean? Does $_{11}$mean the first example weights 1/50 to first class, say, Iris Setosa?
 A: In weighted nearest neighbour, all of the points in the dataset have a contribution, which is quantified by $w_{ni}$ in your references. So, in this version, there is no top $k$. Every point in the dataset has a saying on the outcome. And, KNN can also be considered as a special case of weighted NN where $w_{ni}=1/k$ when $1\leq i\leq k$, and $0$ otherwise. In regression, these weights can be directly incorporated to the outcome, i.e. $$\hat{y}=\sum_{i=1}^nw_{ni}y_i$$
But in classification, you'll count votes together with weights, i.e. the cumulative vote for class $m$ is calculated as follows: $$c_m=\sum_{i=1}^nw_{ni}\underbrace{\mathbf{1}[y_i=m]}_{\text{indicator function}}=\sum_{y_i=m}w_{ni}$$
In the end, you'll compare the votes on classes. And, decide the class with the highest vote.
Taking your example, i.e. the iris dataset, and a KNN with $k=50$, we have $w_{ni}=1/50$ for $1\leq i \leq 50$, as you noted. So, the top $50$ nearest neighbors have equal vote on the outcome. Iris dataset has three classes, so you'll calculate $c_1,c_2,c_3$ and choose the one with the highest value.
