Diffuse polarized neutron scattering studies have been carried out on single crystals of pyrochlore spin ice Ho_2-xY_xTi₂O₇ (x=0, 0.3, and 1) to investigate the effects of doping and an isotropy on spin correlations in the system. The crystals were aligned with the (1 -1 0) orientation coincident with the direction of neutron polarization. For all the samples studied the spin flip(SF) diffuse scattering (i.e. the in-plane component) reveals that the spin correlation scan be described using a nearest-neighbour spin ice model (NNSM) at higher temperatures (T=3.6 K) and a dipolar spin ice model(DSM) as the temperature is reduced (T=30 mK). In the non-spin flip (NSF) channel (i.e. the out-of-plane component), the signature of strong anti ferromagnetic correlations is observed for all the samples at the same temperature as the dipolar spin ice behavior appears in the SF channel. Our studies show that the non-magnetic dopant Y  does not significantly alter SF or NSF scattering for the spin ice state, even when Y doping is as high as 50%. In this paper, we focus on the experimental results of the highly doped spin ice HoYTi₂O₇ and compare our results with pure spin ice Ho₂Ti₂O₇. The cross over from a dipolar to a nearest- neighbour spin ice  behavior and the doping in sensitivity in spin ices are briefly discussed.